ðŸ‘‰ Try now NerdPal! Our new math app on iOS and Android

# Square of a Trinomial Calculator

## Get detailed solutions to your math problems with our Square of a Trinomial step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here.

Go!
Symbolic mode
Text mode
Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

###  Difficult Problems

1

Here, we show you a step-by-step solved example of square of a trinomial. This solution was automatically generated by our smart calculator:

$f\left(x\right)=\left(8x^2-3x+2\right)^3$

Expand the cube of a trinomial

$f\left(x\right)=\left(8x^2\right)^3+3\cdot -3\left(8x^2\right)^2x+3\cdot 2\left(8x^2\right)^2+\left(-3x\right)^3+3\cdot 8x^2\left(-3x\right)^2+3\cdot 2\left(-3x\right)^2+2^3+3\cdot 8\cdot 2^2x^2+3\cdot -3\cdot 2^2x+6\cdot 8\cdot -3\cdot 2x^2x$

Multiply $3$ times $-3$

$f\left(x\right)=\left(8x^2\right)^3-9\left(8x^2\right)^2x+3\cdot 2\left(8x^2\right)^2+\left(-3x\right)^3+3\cdot 8x^2\left(-3x\right)^2+3\cdot 2\left(-3x\right)^2+2^3+3\cdot 8\cdot 2^2x^2+3\cdot -3\cdot 2^2x+6\cdot 8\cdot -3\cdot 2x^2x$

Multiply $3$ times $2$

$f\left(x\right)=\left(8x^2\right)^3-9\left(8x^2\right)^2x+6\left(8x^2\right)^2+\left(-3x\right)^3+3\cdot 8x^2\left(-3x\right)^2+3\cdot 2\left(-3x\right)^2+2^3+3\cdot 8\cdot 2^2x^2+3\cdot -3\cdot 2^2x+6\cdot 8\cdot -3\cdot 2x^2x$

Multiply $3$ times $8$

$f\left(x\right)=\left(8x^2\right)^3-9\left(8x^2\right)^2x+6\left(8x^2\right)^2+\left(-3x\right)^3+24x^2\left(-3x\right)^2+3\cdot 2\left(-3x\right)^2+2^3+3\cdot 8\cdot 2^2x^2+3\cdot -3\cdot 2^2x+6\cdot 8\cdot -3\cdot 2x^2x$

Multiply $3$ times $2$

$f\left(x\right)=\left(8x^2\right)^3-9\left(8x^2\right)^2x+6\left(8x^2\right)^2+\left(-3x\right)^3+24x^2\left(-3x\right)^2+6\left(-3x\right)^2+2^3+3\cdot 8\cdot 2^2x^2+3\cdot -3\cdot 2^2x+6\cdot 8\cdot -3\cdot 2x^2x$

Multiply $3$ times $8$

$f\left(x\right)=\left(8x^2\right)^3-9\left(8x^2\right)^2x+6\left(8x^2\right)^2+\left(-3x\right)^3+24x^2\left(-3x\right)^2+6\left(-3x\right)^2+2^3+24\cdot 2^2x^2+3\cdot -3\cdot 2^2x+6\cdot 8\cdot -3\cdot 2x^2x$

Multiply $3$ times $-3$

$f\left(x\right)=\left(8x^2\right)^3-9\left(8x^2\right)^2x+6\left(8x^2\right)^2+\left(-3x\right)^3+24x^2\left(-3x\right)^2+6\left(-3x\right)^2+2^3+24\cdot 2^2x^2-9\cdot 2^2x+6\cdot 8\cdot -3\cdot 2x^2x$

Multiply $6$ times $8$

$f\left(x\right)=\left(8x^2\right)^3-9\left(8x^2\right)^2x+6\left(8x^2\right)^2+\left(-3x\right)^3+24x^2\left(-3x\right)^2+6\left(-3x\right)^2+2^3+24\cdot 2^2x^2-9\cdot 2^2x+48\cdot -3\cdot 2x^2x$

Multiply $48$ times $-3$

$f\left(x\right)=\left(8x^2\right)^3-9\left(8x^2\right)^2x+6\left(8x^2\right)^2+\left(-3x\right)^3+24x^2\left(-3x\right)^2+6\left(-3x\right)^2+2^3+24\cdot 2^2x^2-9\cdot 2^2x-144\cdot 2x^2x$

Multiply $-144$ times $2$

$f\left(x\right)=\left(8x^2\right)^3-9\left(8x^2\right)^2x+6\left(8x^2\right)^2+\left(-3x\right)^3+24x^2\left(-3x\right)^2+6\left(-3x\right)^2+2^3+24\cdot 2^2x^2-9\cdot 2^2x-288x^2x$

Calculate the power $2^3$

$f\left(x\right)=\left(8x^2\right)^3-9\left(8x^2\right)^2x+6\left(8x^2\right)^2+\left(-3x\right)^3+24x^2\left(-3x\right)^2+6\left(-3x\right)^2+8+24\cdot 4x^2-9\cdot 4x-288x^2x$

Multiply $24$ times $4$

$f\left(x\right)=\left(8x^2\right)^3-9\left(8x^2\right)^2x+6\left(8x^2\right)^2+\left(-3x\right)^3+24x^2\left(-3x\right)^2+6\left(-3x\right)^2+8+96x^2-9\cdot 4x-288x^2x$

Multiply $-9$ times $4$

$f\left(x\right)=\left(8x^2\right)^3-9\left(8x^2\right)^2x+6\left(8x^2\right)^2+\left(-3x\right)^3+24x^2\left(-3x\right)^2+6\left(-3x\right)^2+8+96x^2-36x-288x^2x$
2

Expand the cube of a trinomial

$f\left(x\right)=\left(8x^2\right)^3-9\left(8x^2\right)^2x+6\left(8x^2\right)^2+\left(-3x\right)^3+24x^2\left(-3x\right)^2+6\left(-3x\right)^2+8+96x^2-36x-288x^2x$

When multiplying exponents with same base you can add the exponents: $-288x^2x$

$f\left(x\right)=\left(8x^2\right)^3-9\left(8x^2\right)^2x+6\left(8x^2\right)^2+\left(-3x\right)^3+24x^2\left(-3x\right)^2+6\left(-3x\right)^2+8+96x^2-36x-288x^{2+1}$

Add the values $2$ and $1$

$f\left(x\right)=\left(8x^2\right)^3-9\left(8x^2\right)^2x+6\left(8x^2\right)^2+\left(-3x\right)^3+24x^2\left(-3x\right)^2+6\left(-3x\right)^2+8+96x^2-36x-288x^{3}$
3

When multiplying exponents with same base you can add the exponents: $-288x^2x$

$f\left(x\right)=\left(8x^2\right)^3-9\left(8x^2\right)^2x+6\left(8x^2\right)^2+\left(-3x\right)^3+24x^2\left(-3x\right)^2+6\left(-3x\right)^2+8+96x^2-36x-288x^{3}$

The power of a product is equal to the product of it's factors raised to the same power

$f\left(x\right)=512x^{6}-9\cdot 64x^{4}x+6\cdot 8^2\left(x^2\right)^2+\left(-3x\right)^3+24x^2\left(-3x\right)^2+6\left(-3x\right)^2+8+96x^2-36x-288x^{3}$

The power of a product is equal to the product of it's factors raised to the same power

$f\left(x\right)=512x^{6}-9x8^2\left(x^2\right)^2+6\left(8x^2\right)^2+\left(-3x\right)^3+24x^2\left(-3x\right)^2+6\left(-3x\right)^2+8+96x^2-36x-288x^{3}$

$f\left(x\right)=8^3\left(x^2\right)^3-9\left(8x^2\right)^2x+6\left(8x^2\right)^2+\left(-3x\right)^3+24x^2\left(-3x\right)^2+6\left(-3x\right)^2+8+96x^2-36x-288x^{3}$

Calculate the power $8^3$

$f\left(x\right)=512\left(x^2\right)^3-9\left(8x^2\right)^2x+6\left(8x^2\right)^2+\left(-3x\right)^3+24x^2\left(-3x\right)^2+6\left(-3x\right)^2+8+96x^2-36x-288x^{3}$

Simplify $\left(x^2\right)^3$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $2$ and $n$ equals $3$

$512x^{2\cdot 3}$

Multiply $2$ times $3$

$512x^{6}$

Multiply $2$ times $3$

$f\left(x\right)=512x^{6}-9\left(8x^2\right)^2x+6\left(8x^2\right)^2+\left(-3x\right)^3+24x^2\left(-3x\right)^2+6\left(-3x\right)^2+8+96x^2-36x-288x^{3}$

Calculate the power $8^2$

$f\left(x\right)=512x^{6}-9x64\left(x^2\right)^2+6\left(8x^2\right)^2+\left(-3x\right)^3+24x^2\left(-3x\right)^2+6\left(-3x\right)^2+8+96x^2-36x-288x^{3}$

Simplify $\left(x^2\right)^3$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $2$ and $n$ equals $3$

$512x^{2\cdot 3}$

Multiply $2$ times $3$

$512x^{6}$

Simplify $\left(x^2\right)^2$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $2$ and $n$ equals $2$

$64x^{2\cdot 2}$

Multiply $2$ times $2$

$64x^{4}$

Multiply $2$ times $2$

$f\left(x\right)=512x^{6}-9x64x^{4}+6\left(8x^2\right)^2+\left(-3x\right)^3+24x^2\left(-3x\right)^2+6\left(-3x\right)^2+8+96x^2-36x-288x^{3}$

The power of a product is equal to the product of it's factors raised to the same power

$f\left(x\right)=512x^{6}-9\cdot 64x^{4}x+6\left(8x^2\right)^2+\left(-3x\right)^3+24x^2\left(-3x\right)^2+6\left(-3x\right)^2+8+96x^2-36x-288x^{3}$

Calculate the power $8^2$

$f\left(x\right)=512x^{6}-9\cdot 64x^{4}x+6\cdot 64\left(x^2\right)^2+\left(-3x\right)^3+24x^2\left(-3x\right)^2+6\left(-3x\right)^2+8+96x^2-36x-288x^{3}$

Simplify $\left(x^2\right)^3$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $2$ and $n$ equals $3$

$512x^{2\cdot 3}$

Multiply $2$ times $3$

$512x^{6}$

Simplify $\left(x^2\right)^2$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $2$ and $n$ equals $2$

$64x^{2\cdot 2}$

Multiply $2$ times $2$

$64x^{4}$

Simplify $\left(x^2\right)^2$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $2$ and $n$ equals $2$

$64x^{2\cdot 2}$

Multiply $2$ times $2$

$64x^{4}$

Multiply $2$ times $2$

$f\left(x\right)=512x^{6}-9\cdot 64x^{4}x+6\cdot 64x^{4}+\left(-3x\right)^3+24x^2\left(-3x\right)^2+6\left(-3x\right)^2+8+96x^2-36x-288x^{3}$

The power of a product is equal to the product of it's factors raised to the same power

$f\left(x\right)=512x^{6}-9\cdot 64x^{4}x+6\cdot 64x^{4}+\left(-3x\right)^3+24x^2\left(-3x\right)^2+6\left(-3x\right)^2+8+96x^2-36x-288x^{3}$
4

The power of a product is equal to the product of it's factors raised to the same power

$f\left(x\right)=512x^{6}-9\cdot 64x^{4}x+6\cdot 64x^{4}+\left(-3x\right)^3+24x^2\left(-3x\right)^2+6\left(-3x\right)^2+8+96x^2-36x-288x^{3}$
5

Multiply $-9$ times $64$

$f\left(x\right)=512x^{6}-576x^{4}x+6\cdot 64x^{4}+\left(-3x\right)^3+24x^2\left(-3x\right)^2+6\left(-3x\right)^2+8+96x^2-36x-288x^{3}$
6

Multiply $6$ times $64$

$f\left(x\right)=512x^{6}-576x^{4}x+384x^{4}+\left(-3x\right)^3+24x^2\left(-3x\right)^2+6\left(-3x\right)^2+8+96x^2-36x-288x^{3}$

When multiplying exponents with same base you can add the exponents: $-576x^{4}x$

$f\left(x\right)=512x^{6}-576x^{4+1}+384x^{4}+\left(-3x\right)^3+24x^2\left(-3x\right)^2+6\left(-3x\right)^2+8+96x^2-36x-288x^{3}$

When multiplying exponents with same base you can add the exponents: $-288x^2x$

$f\left(x\right)=\left(8x^2\right)^3-9\left(8x^2\right)^2x+6\left(8x^2\right)^2+\left(-3x\right)^3+24x^2\left(-3x\right)^2+6\left(-3x\right)^2+8+96x^2-36x-288x^{2+1}$

Add the values $2$ and $1$

$f\left(x\right)=\left(8x^2\right)^3-9\left(8x^2\right)^2x+6\left(8x^2\right)^2+\left(-3x\right)^3+24x^2\left(-3x\right)^2+6\left(-3x\right)^2+8+96x^2-36x-288x^{3}$

Add the values $4$ and $1$

$f\left(x\right)=512x^{6}-576x^{5}+384x^{4}+\left(-3x\right)^3+24x^2\left(-3x\right)^2+6\left(-3x\right)^2+8+96x^2-36x-288x^{3}$
7

When multiplying exponents with same base you can add the exponents: $-576x^{4}x$

$f\left(x\right)=512x^{6}-576x^{5}+384x^{4}+\left(-3x\right)^3+24x^2\left(-3x\right)^2+6\left(-3x\right)^2+8+96x^2-36x-288x^{3}$

##  Final answer to the problem

$f\left(x\right)=512x^{6}-576x^{5}+384x^{4}+\left(-3x\right)^3+24x^2\left(-3x\right)^2+6\left(-3x\right)^2+8+96x^2-36x-288x^{3}$

### Are you struggling with math?

Access detailed step by step solutions to thousands of problems, growing every day!