Solve f(x)=5(x+5)^2(x-5)(x^2-49)

$$f ( x ) = 5 ( x + 5 ) ^ { 2 } ( x - 5 ) ( x ^ { 2 } - 49 )$$

Evaluate

$$5\left(x-5\right)\left(x^{2}-49\right)\left(x+5\right)^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+5\right)^{2}.

$$5\left(x^{2}+10x+25\right)\left(x-5\right)\left(x^{2}-49\right)$$

Use the distributive property to multiply 5 by x^{2}+10x+25.

$$\left(5x^{2}+50x+125\right)\left(x-5\right)\left(x^{2}-49\right)$$

Use the distributive property to multiply 5x^{2}+50x+125 by x-5 and combine like terms.

$$\left(5x^{3}+25x^{2}-125x-625\right)\left(x^{2}-49\right)$$

Use the distributive property to multiply 5x^{3}+25x^{2}-125x-625 by x^{2}-49 and combine like terms.

$$5x^{5}-370x^{3}+25x^{4}-1850x^{2}+6125x+30625$$

Expand

$$5x^{5}+25x^{4}-370x^{3}-1850x^{2}+6125x+30625$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+5\right)^{2}.

$$5\left(x^{2}+10x+25\right)\left(x-5\right)\left(x^{2}-49\right)$$

Use the distributive property to multiply 5 by x^{2}+10x+25.

$$\left(5x^{2}+50x+125\right)\left(x-5\right)\left(x^{2}-49\right)$$

Use the distributive property to multiply 5x^{2}+50x+125 by x-5 and combine like terms.

$$\left(5x^{3}+25x^{2}-125x-625\right)\left(x^{2}-49\right)$$

Use the distributive property to multiply 5x^{3}+25x^{2}-125x-625 by x^{2}-49 and combine like terms.

$$5x^{5}-370x^{3}+25x^{4}-1850x^{2}+6125x+30625$$