Square of a Trinomial Calculator

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 Example

 Solved Problems

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

$f\left(x\right)=\left(1+4x-2x^2\right)^2$

Expand the trinomial using the formula $\left(a+b+c\right)^2 = a^2 + b^2 + c^2 + 2ab + 2ac + 2bc$

$f\left(x\right)=1^2+\left(4x\right)^2+\left(-2x^2\right)^2+2\cdot 1\cdot 4x+2\cdot 1\cdot -2x^2+2\cdot 4\cdot -2xx^2$

Any expression multiplied by $1$ is equal to itself

$f\left(x\right)=1^2+\left(4x\right)^2+\left(-2x^2\right)^2+2\cdot 4x+2\cdot 1\cdot -2x^2+2\cdot 4\cdot -2xx^2$

Any expression multiplied by $1$ is equal to itself

$f\left(x\right)=1^2+\left(4x\right)^2+\left(-2x^2\right)^2+2\cdot 4x+2\cdot -2x^2+2\cdot 4\cdot -2xx^2$

Multiply $2$ times $4$

$f\left(x\right)=1^2+\left(4x\right)^2+\left(-2x^2\right)^2+8x+2\cdot -2x^2+2\cdot 4\cdot -2xx^2$

Multiply $2$ times $-2$

$f\left(x\right)=1^2+\left(4x\right)^2+\left(-2x^2\right)^2+8x-4x^2+2\cdot 4\cdot -2xx^2$

Multiply $2$ times $4$

$f\left(x\right)=1^2+\left(4x\right)^2+\left(-2x^2\right)^2+8x-4x^2+8\cdot -2xx^2$

Multiply $8$ times $-2$

$f\left(x\right)=1^2+\left(4x\right)^2+\left(-2x^2\right)^2+8x-4x^2-16x\cdot x^2$

Calculate the power $1^2$

$f\left(x\right)=1+\left(4x\right)^2+\left(-2x^2\right)^2+8x-4x^2-16x\cdot x^2$

Expand the trinomial using the formula $\left(a+b+c\right)^2 = a^2 + b^2 + c^2 + 2ab + 2ac + 2bc$

$f\left(x\right)=1+\left(4x\right)^2+\left(-2x^2\right)^2+8x-4x^2-16x\cdot x^2$

When multiplying exponents with same base you can add the exponents: $-16x\cdot x^2$

$f\left(x\right)=1+\left(4x\right)^2+\left(-2x^2\right)^2+8x-4x^2-16x^{2+1}$

Add the values $2$ and $1$

$f\left(x\right)=1+\left(4x\right)^2+\left(-2x^2\right)^2+8x-4x^2-16x^{3}$

When multiplying exponents with same base you can add the exponents: $-16x\cdot x^2$

$f\left(x\right)=1+\left(4x\right)^2+\left(-2x^2\right)^2+8x-4x^2-16x^{3}$

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

$f\left(x\right)=1+4^2x^2+\left(-2x^2\right)^2+8x-4x^2-16x^{3}$

Calculate the power $4^2$

$f\left(x\right)=1+16x^2+\left(-2x^2\right)^2+8x-4x^2-16x^{3}$

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

$f\left(x\right)=1+16x^2+\left(-2x^2\right)^2+8x-4x^2-16x^{3}$

Combining like terms $16x^2$ and $-4x^2$

$f\left(x\right)=1+12x^2+\left(-2x^2\right)^2+8x-16x^{3}$

 Final answer to the problem