Solve A=x^4left(x^2-25right)-10x^2left(x^2-25right)-9left({x}^2-25right)

$$A = { x }^{ 4 } \left( { x }^{ 2 } -25 \right) -10 { x }^{ 2 } \left( { x }^{ 2 } -25 \right) -9 \left( { x }^{ 2 } -25 \right)$$

Solve for A

$$A=x^{6}-35x^{4}+241x^{2}+225$$

Solution Steps

Use the distributive property to multiply x^{4} by x^{2}-25.

$$A=x^{6}-25x^{4}-10x^{2}\left(x^{2}-25\right)-9\left(x^{2}-25\right)$$

Use the distributive property to multiply -9 by x^{2}-25.

$$A=x^{6}-25x^{4}-10x^{2}\left(x^{2}-25\right)-9x^{2}+225$$

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

$$A=x^{6}-25x^{4}-10x^{4}+250x^{2}-9x^{2}+225$$

Combine -25x^{4} and -10x^{4} to get -35x^{4}.

$$A=x^{6}-35x^{4}+250x^{2}-9x^{2}+225$$

Combine 250x^{2} and -9x^{2} to get 241x^{2}.

$$A=x^{6}-35x^{4}+241x^{2}+225$$