Solve h(x)=5(x+3)^2(x^2-36)(x-3)

$$h ( x ) = 5 ( x + 3 ) ^ { 2 } ( x ^ { 2 } - 36 ) ( x - 3 )$$

Evaluate

$$5\left(x-3\right)\left(x^{2}-36\right)\left(x+3\right)^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+3\right)^{2}.

$$5\left(x^{2}+6x+9\right)\left(x^{2}-36\right)\left(x-3\right)$$

Use the distributive property to multiply 5 by x^{2}+6x+9.

$$\left(5x^{2}+30x+45\right)\left(x^{2}-36\right)\left(x-3\right)$$

Use the distributive property to multiply 5x^{2}+30x+45 by x^{2}-36 and combine like terms.

$$\left(5x^{4}-135x^{2}+30x^{3}-1080x-1620\right)\left(x-3\right)$$

Use the distributive property to multiply 5x^{4}-135x^{2}+30x^{3}-1080x-1620 by x-3 and combine like terms.

$$5x^{5}+15x^{4}-225x^{3}-675x^{2}+1620x+4860$$

Expand

$$5x^{5}+15x^{4}-225x^{3}-675x^{2}+1620x+4860$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+3\right)^{2}.

$$5\left(x^{2}+6x+9\right)\left(x^{2}-36\right)\left(x-3\right)$$

Use the distributive property to multiply 5 by x^{2}+6x+9.

$$\left(5x^{2}+30x+45\right)\left(x^{2}-36\right)\left(x-3\right)$$

Use the distributive property to multiply 5x^{2}+30x+45 by x^{2}-36 and combine like terms.

$$\left(5x^{4}-135x^{2}+30x^{3}-1080x-1620\right)\left(x-3\right)$$

Use the distributive property to multiply 5x^{4}-135x^{2}+30x^{3}-1080x-1620 by x-3 and combine like terms.

$$5x^{5}+15x^{4}-225x^{3}-675x^{2}+1620x+4860$$