[tex] \huge \boxed{\mathbb{QUESTION} \downarrow}[/tex]
- Solve ⇨ (x + 1)(x + 2) • (x + 2)(x - 2)
[tex] \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}[/tex]
[tex]( x + 1 ) ( x + 2 ) \cdot ( x + 2 ) ( x - 2 )[/tex]
Multiply x+2 and x+2 to get [tex]\left(x+2\right)^{2}[/tex].
[tex]\left(x+1\right)\left(x+2\right)^{2}\left(x-2\right) [/tex]
Use binomial theorem [tex]\left(a+b\right)^{2}=a^{2}+2ab+b^{2} [/tex] to expand [tex]\left(x+2\right)^{2}[/tex].
[tex]\left(x+1\right)\left(x^{2}+4x+4\right)\left(x-2\right) [/tex]
Apply the distributive property by multiplying each term of x+1 by each term of x²+4x+4.
[tex]\left(x^{3}+4x^{2}+4x+x^{2}+4x+4\right)\left(x-2\right) [/tex]
Combine 4x² and x² to get 5x².
[tex]\left(x^{3}+5x^{2}+4x+4x+4\right)\left(x-2\right) [/tex]
Combine 4x and 4x to get 8x.
[tex]\left(x^{3}+5x^{2}+8x+4\right)\left(x-2\right) [/tex]
Apply the distributive property by multiplying each term of x³+5x²+8x+4 by each term of x-2.
[tex]x^{4}-2x^{3}+5x^{3}-10x^{2}+8x^{2}-16x+4x-8 [/tex]
Combine -2x³ and 5x³ to get 3x³.
[tex]x^{4}+3x^{3}-10x^{2}+8x^{2}-16x+4x-8 [/tex]
Combine -10x² and 8x² to get -2x².
[tex]x^{4}+3x^{3}-2x^{2}-16x+4x-8 [/tex]
Combine -16x and 4x to get -12x.
[tex] \large \boxed{ \boxed{\bf \: x^{4}+3x^{3}-2x^{2}-12x-8 }}[/tex]
