Solve x^2-8x(x-3y)+16(x-3y)^2=

$$x ^ { 2 } - 8 x ( x - 3 y ) + 16 ( x - 3 y ) ^ { 2 } =$$

Evaluate

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

Solution Steps

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

$$x^{2}-8x\left(x-3y\right)+16\left(x^{2}-6xy+9y^{2}\right)$$

Use the distributive property to multiply 16 by x^{2}-6xy+9y^{2}.

$$x^{2}-8x\left(x-3y\right)+16x^{2}-96xy+144y^{2}$$

Use the distributive property to multiply -8x by x-3y.

$$x^{2}-8x^{2}+24xy+16x^{2}-96xy+144y^{2}$$

Combine x^{2} and -8x^{2} to get -7x^{2}.

$$-7x^{2}+24xy+16x^{2}-96xy+144y^{2}$$

Combine -7x^{2} and 16x^{2} to get 9x^{2}.

$$9x^{2}+24xy-96xy+144y^{2}$$

Combine 24xy and -96xy to get -72xy.

$$9x^{2}-72xy+144y^{2}$$

Expand

$$9x^{2}-72xy+144y^{2}$$

Solution Steps

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

$$x^{2}-8x\left(x-3y\right)+16\left(x^{2}-6xy+9y^{2}\right)$$

Use the distributive property to multiply 16 by x^{2}-6xy+9y^{2}.

$$x^{2}-8x\left(x-3y\right)+16x^{2}-96xy+144y^{2}$$

Use the distributive property to multiply -8x by x-3y.

$$x^{2}-8x^{2}+24xy+16x^{2}-96xy+144y^{2}$$

Combine x^{2} and -8x^{2} to get -7x^{2}.

$$-7x^{2}+24xy+16x^{2}-96xy+144y^{2}$$

Combine -7x^{2} and 16x^{2} to get 9x^{2}.

$$9x^{2}+24xy-96xy+144y^{2}$$

Combine 24xy and -96xy to get -72xy.

$$9x^{2}-72xy+144y^{2}$$