Solve (4+x)^2+(4+y)^2

$$( 4 + x ) ^ { 2 } + ( 4 + y ) ^ { 2 }$$

Evaluate

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

Solution Steps

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

$$16+8x+x^{2}+\left(4+y\right)^{2}$$

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

$$16+8x+x^{2}+16+8y+y^{2}$$

Add 16 and 16 to get 32.

$$32+8x+x^{2}+8y+y^{2}$$

Expand

$$x^{2}+8x+y^{2}+8y+32$$

Solution Steps

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

$$16+8x+x^{2}+\left(4+y\right)^{2}$$

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

$$16+8x+x^{2}+16+8y+y^{2}$$

Add 16 and 16 to get 32.

$$32+8x+x^{2}+8y+y^{2}$$