Solve 25(x-2)^2-9(x+2)^2

$$25 ( x - 2 ) ^ { 2 } - 9 ( x + 2 ) ^ { 2 }$$

Evaluate

$$8\left(x-8\right)\left(2x-1\right)$$

Solution Steps

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

$$25\left(x^{2}-4x+4\right)-9\left(x+2\right)^{2}$$

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

$$25x^{2}-100x+100-9\left(x+2\right)^{2}$$

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

$$25x^{2}-100x+100-9\left(x^{2}+4x+4\right)$$

Use the distributive property to multiply -9 by x^{2}+4x+4.

$$25x^{2}-100x+100-9x^{2}-36x-36$$

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

$$16x^{2}-100x+100-36x-36$$

Combine -100x and -36x to get -136x.

$$16x^{2}-136x+100-36$$

Subtract 36 from 100 to get 64.

$$16x^{2}-136x+64$$

Expand

$$16x^{2}-136x+64$$

Solution Steps

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

$$25\left(x^{2}-4x+4\right)-9\left(x+2\right)^{2}$$

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

$$25x^{2}-100x+100-9\left(x+2\right)^{2}$$

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

$$25x^{2}-100x+100-9\left(x^{2}+4x+4\right)$$

Use the distributive property to multiply -9 by x^{2}+4x+4.

$$25x^{2}-100x+100-9x^{2}-36x-36$$

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

$$16x^{2}-100x+100-36x-36$$

Combine -100x and -36x to get -136x.

$$16x^{2}-136x+100-36$$

Subtract 36 from 100 to get 64.

$$16x^{2}-136x+64$$