Solve (x+y)^2-14(x+y)+49

$$( x + y ) ^ { 2 } - 14 ( x + y ) + 49$$

Evaluate

$$\left(x+y-7\right)^{2}$$

Solution Steps

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

$$x^{2}+2xy+y^{2}-14\left(x+y\right)+49$$

Use the distributive property to multiply -14 by x+y.

$$x^{2}+2xy+y^{2}-14x-14y+49$$

Expand

$$x^{2}+2xy-14x+y^{2}-14y+49$$

Solution Steps

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

$$x^{2}+2xy+y^{2}-14\left(x+y\right)+49$$

Use the distributive property to multiply -14 by x+y.

$$x^{2}+2xy+y^{2}-14x-14y+49$$