Solve 3(3x-y)^2-12z^2

$$3 ( 3 x - y ) ^ { 2 } - 12 z ^ { 2 }$$

Evaluate

$$3\left(\left(y-3x\right)^{2}-4z^{2}\right)$$

Solution Steps

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

$$3\left(9x^{2}-6xy+y^{2}\right)-12z^{2}$$

Use the distributive property to multiply 3 by 9x^{2}-6xy+y^{2}.

$$27x^{2}-18xy+3y^{2}-12z^{2}$$

Expand

$$27x^{2}-18xy+3y^{2}-12z^{2}$$

Solution Steps

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

$$3\left(9x^{2}-6xy+y^{2}\right)-12z^{2}$$

Use the distributive property to multiply 3 by 9x^{2}-6xy+y^{2}.

$$27x^{2}-18xy+3y^{2}-12z^{2}$$