Solve 11*(x+y)^2-4(x+y-1)

$$11 \cdot ( x + y ) ^ { 2 } - 4 ( x + y - 1 )$$

Evaluate

$$11\left(x+y\right)^{2}-4x-4y+4$$

Solution Steps

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

$$11\left(x^{2}+2xy+y^{2}\right)-4\left(x+y-1\right)$$

Use the distributive property to multiply 11 by x^{2}+2xy+y^{2}.

$$11x^{2}+22xy+11y^{2}-4\left(x+y-1\right)$$

Use the distributive property to multiply -4 by x+y-1.

$$11x^{2}+22xy+11y^{2}-4x-4y+4$$

Expand

$$11x^{2}+22xy-4x+11y^{2}-4y+4$$

Solution Steps

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

$$11\left(x^{2}+2xy+y^{2}\right)-4\left(x+y-1\right)$$

Use the distributive property to multiply 11 by x^{2}+2xy+y^{2}.

$$11x^{2}+22xy+11y^{2}-4\left(x+y-1\right)$$

Use the distributive property to multiply -4 by x+y-1.

$$11x^{2}+22xy+11y^{2}-4x-4y+4$$