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Expand the expression $\left(3x+5\right)\left(2x+3\right)$

Step-by-step Solution

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Final answer to the problem

$6x^2+19x+15$
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Step-by-step Solution

How should I solve this problem?

  • FOIL Method
  • Product of Binomials with Common Term
  • Find the integral
  • Find the derivative
  • Factor
  • Integrate by partial fractions
  • Integrate by substitution
  • Integrate by parts
  • Integrate using tabular integration
  • Integrate by trigonometric substitution
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Can't find a method? Tell us so we can add it.
1

We can multiply the polynomials $\left(3x+5\right)\left(2x+3\right)$ by using the FOIL method. The acronym F O I L stands for multiplying the terms in each bracket in the following order: First by First ($F\times F$), Outer by Outer ($O\times O$), Inner by Inner ($I\times I$), Last by Last ($L\times L$)

$\begin{matrix}(F\times F)\:=\:(3x)(2x)\\(O\times O)\:=\:(3x)(3)\\(I\times I)\:=\:(5)(2x)\\(L\times L)\:=\:(5)(3)\end{matrix}$
2

Then, combine the four terms in a sum

$(F\times F) + (O\times O) + (I\times I) + (L\times L)$
3

Substitute the values of the products

$3x2x+3\cdot 3x+5\cdot 2x+5\cdot 3$
4

Multiply $5$ times $3$

$3\cdot 2x\cdot x+3\cdot 3x+5\cdot 2x+15$
5

Multiply $3$ times $2$

$6x\cdot x+3\cdot 3x+5\cdot 2x+15$
6

Multiply $3$ times $3$

$6x\cdot x+9x+5\cdot 2x+15$
7

Multiply $5$ times $2$

$6x\cdot x+9x+10x+15$
8

Combining like terms $9x$ and $10x$

$6x\cdot x+19x+15$
9

When multiplying two powers that have the same base ($x$), you can add the exponents

$6x^2+19x+15$

Final answer to the problem

$6x^2+19x+15$

Explore different ways to solve this problem

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Plotting: $6x^2+19x+15$

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5
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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

How to improve your answer:

Main Topic: Trigonometric Integrals

Integrals that contain trigonometric functions and their powers.

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