Solve 25x^2-(3x-y)^2

$$25 x ^ { 2 } - ( 3 x - y ) ^ { 2 }$$

Evaluate

$$\left(8x-y\right)\left(2x+y\right)$$

Solution Steps

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

$$25x^{2}-\left(9x^{2}-6xy+y^{2}\right)$$

To find the opposite of 9x^{2}-6xy+y^{2}, find the opposite of each term.

$$25x^{2}-9x^{2}+6xy-y^{2}$$

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

$$16x^{2}+6xy-y^{2}$$

Expand

$$16x^{2}+6xy-y^{2}$$

Solution Steps

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

$$25x^{2}-\left(9x^{2}-6xy+y^{2}\right)$$

To find the opposite of 9x^{2}-6xy+y^{2}, find the opposite of each term.

$$25x^{2}-9x^{2}+6xy-y^{2}$$

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

$$16x^{2}+6xy-y^{2}$$