Solve (4x-3y)^2+2(3y-4x)+1

$$( 4 x - 3 y ) ^ { 2 } + 2 ( 3 y - 4 x ) + 1$$

Evaluate

$$\left(4x-3y-1\right)^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(4x-3y\right)^{2}.

$$16x^{2}-24xy+9y^{2}+2\left(3y-4x\right)+1$$

Use the distributive property to multiply 2 by 3y-4x.

$$16x^{2}-24xy+9y^{2}+6y-8x+1$$

Expand

$$16x^{2}-24xy-8x+9y^{2}+6y+1$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(4x-3y\right)^{2}.

$$16x^{2}-24xy+9y^{2}+2\left(3y-4x\right)+1$$

Use the distributive property to multiply 2 by 3y-4x.

$$16x^{2}-24xy+9y^{2}+6y-8x+1$$