Solve 25(x-1)^2-16(x+2)^2

$$25 ( x - 1 ) ^ { 2 } - 16 ( x + 2 ) ^ { 2 }$$

Evaluate

$$3\left(x-13\right)\left(3x+1\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

$$25\left(x^{2}-2x+1\right)-16\left(x+2\right)^{2}$$

Use the distributive property to multiply 25 by x^{2}-2x+1.

$$25x^{2}-50x+25-16\left(x+2\right)^{2}$$

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

$$25x^{2}-50x+25-16\left(x^{2}+4x+4\right)$$

Use the distributive property to multiply -16 by x^{2}+4x+4.

$$25x^{2}-50x+25-16x^{2}-64x-64$$

Combine 25x^{2} and -16x^{2} to get 9x^{2}.

$$9x^{2}-50x+25-64x-64$$

Combine -50x and -64x to get -114x.

$$9x^{2}-114x+25-64$$

Subtract 64 from 25 to get -39.

$$9x^{2}-114x-39$$

Expand

$$9x^{2}-114x-39$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

$$25\left(x^{2}-2x+1\right)-16\left(x+2\right)^{2}$$

Use the distributive property to multiply 25 by x^{2}-2x+1.

$$25x^{2}-50x+25-16\left(x+2\right)^{2}$$

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

$$25x^{2}-50x+25-16\left(x^{2}+4x+4\right)$$

Use the distributive property to multiply -16 by x^{2}+4x+4.

$$25x^{2}-50x+25-16x^{2}-64x-64$$

Combine 25x^{2} and -16x^{2} to get 9x^{2}.

$$9x^{2}-50x+25-64x-64$$

Combine -50x and -64x to get -114x.

$$9x^{2}-114x+25-64$$

Subtract 64 from 25 to get -39.

$$9x^{2}-114x-39$$