Solve (x+4)^2*(x+1)*(x-2)*(x-5)

$$( x + 4 ) ^ { 2 } \cdot ( x + 1 ) \cdot ( x - 2 ) \cdot ( x - 5 )$$

Evaluate

$$\left(x-5\right)\left(x-2\right)\left(x+1\right)\left(x+4\right)^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+4\right)^{2}.

$$\left(x^{2}+8x+16\right)\left(x+1\right)\left(x-2\right)\left(x-5\right)$$

Use the distributive property to multiply x^{2}+8x+16 by x+1 and combine like terms.

$$\left(x^{3}+9x^{2}+24x+16\right)\left(x-2\right)\left(x-5\right)$$

Use the distributive property to multiply x^{3}+9x^{2}+24x+16 by x-2 and combine like terms.

$$\left(x^{4}+7x^{3}+6x^{2}-32x-32\right)\left(x-5\right)$$

Use the distributive property to multiply x^{4}+7x^{3}+6x^{2}-32x-32 by x-5 and combine like terms.

$$x^{5}+2x^{4}-29x^{3}-62x^{2}+128x+160$$

Expand

$$x^{5}+2x^{4}-29x^{3}-62x^{2}+128x+160$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+4\right)^{2}.

$$\left(x^{2}+8x+16\right)\left(x+1\right)\left(x-2\right)\left(x-5\right)$$

Use the distributive property to multiply x^{2}+8x+16 by x+1 and combine like terms.

$$\left(x^{3}+9x^{2}+24x+16\right)\left(x-2\right)\left(x-5\right)$$

Use the distributive property to multiply x^{3}+9x^{2}+24x+16 by x-2 and combine like terms.

$$\left(x^{4}+7x^{3}+6x^{2}-32x-32\right)\left(x-5\right)$$

Use the distributive property to multiply x^{4}+7x^{3}+6x^{2}-32x-32 by x-5 and combine like terms.

$$x^{5}+2x^{4}-29x^{3}-62x^{2}+128x+160$$