Question

="(x + 1)(x + 2).(x + 2)(x - 2)" alt="(x + 1)(x + 2).(x + 2)(x - 2)" align="absmiddle" class="latex-formula">
it is my question ​

Answer 1

$\huge \boxed{\mathbb{QUESTION} \downarrow}$

• Solve ⇨ (x + 1)(x + 2) • (x + 2)(x - 2)

$\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}$

$( x + 1 ) ( x + 2 ) \cdot ( x + 2 ) ( x - 2 )$

Multiply x+2 and x+2 to get $\left(x+2\right)^{2}$.

$\left(x+1\right)\left(x+2\right)^{2}\left(x-2\right)$

Use binomial theorem $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$ to expand $\left(x+2\right)^{2}$.

$\left(x+1\right)\left(x^{2}+4x+4\right)\left(x-2\right)$

Apply the distributive property by multiplying each term of x+1 by each term of x²+4x+4.

$\left(x^{3}+4x^{2}+4x+x^{2}+4x+4\right)\left(x-2\right)$

Combine 4x² and x² to get 5x².

$\left(x^{3}+5x^{2}+4x+4x+4\right)\left(x-2\right)$

Combine 4x and 4x to get 8x.

$\left(x^{3}+5x^{2}+8x+4\right)\left(x-2\right)$

Apply the distributive property by multiplying each term of x³+5x²+8x+4 by each term of x-2.

$x^{4}-2x^{3}+5x^{3}-10x^{2}+8x^{2}-16x+4x-8$

Combine -2x³ and 5x³ to get 3x³.

$x^{4}+3x^{3}-10x^{2}+8x^{2}-16x+4x-8$

Combine -10x² and 8x² to get -2x².

$x^{4}+3x^{3}-2x^{2}-16x+4x-8$

Combine -16x and 4x to get -12x.

$\large \boxed{ \boxed{\bf \: x^{4}+3x^{3}-2x^{2}-12x-8 }}$