What is expand (x+1)^2(x+2)^2 ?

The solution to expand (x+1)^2(x+2)^2 is x^4+6x^3+13x^2+12x+4

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expand (x+1)^2(x+2)^2

expand

(x + 1)^{2} (x + 2)^{2}

x^{4} + 6 x^{3} + 13 x^{2} + 12 x + 4

Solution steps

(x + 1)^{2} (x + 2)^{2}

Expand

(x + 1)^{2} : x^{2} + 2 x + 1

= (x^{2} + 2 x + 1) (x + 2)^{2}

= (x + 2)^{2} (x^{2} + 2 x + 1)

Expand

(x + 2)^{2} : x^{2} + 4 x + 4

= (x^{2} + 4 x + 4) (x^{2} + 2 x + 1)

Distribute parentheses

= x^{2} x^{2} + x^{2} \cdot 2 x + x^{2} \cdot 1 + 4 x x^{2} + 4 x \cdot 2 x + 4 x \cdot 1 + 4 x^{2} + 4 \cdot 2 x + 4 \cdot 1

Simplify

x^{2} x^{2} + x^{2} \cdot 2 x + x^{2} \cdot 1 + 4 x x^{2} + 4 x \cdot 2 x + 4 x \cdot 1 + 4 x^{2} + 4 \cdot 2 x + 4 \cdot 1 : x^{4} + 6 x^{3} + 13 x^{2} + 12 x + 4

= x^{4} + 6 x^{3} + 13 x^{2} + 12 x + 4

\frac{4}{3 + i}

\frac{12 d ^{10}}{3 ( d ^{- 4} ) ^{2}}

x^{4} - 3 x^{2} - 2 x

2 x^{2} - 12 x - 14

2 (x^{2} + 1)

What is expand (x+1)^2(x+2)^2 ?
The solution to expand (x+1)^2(x+2)^2 is x^4+6x^3+13x^2+12x+4