Solve 2(x-6)^2+(a+b)^2-2*(a^2+b^2)=

$$2 ( x - 6 ) ^ { 2 } + ( a + b ) ^ { 2 } - 2 \cdot ( a ^ { 2 } + b ^ { 2 } ) =$$

Evaluate

$$\left(a+b\right)^{2}+2\left(x-6\right)^{2}-2a^{2}-2b^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-6\right)^{2}.

$$2\left(x^{2}-12x+36\right)+\left(a+b\right)^{2}-2\left(a^{2}+b^{2}\right)$$

Use the distributive property to multiply 2 by x^{2}-12x+36.

$$2x^{2}-24x+72+\left(a+b\right)^{2}-2\left(a^{2}+b^{2}\right)$$

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(a+b\right)^{2}.

$$2x^{2}-24x+72+a^{2}+2ab+b^{2}-2\left(a^{2}+b^{2}\right)$$

Use the distributive property to multiply -2 by a^{2}+b^{2}.

$$2x^{2}-24x+72+a^{2}+2ab+b^{2}-2a^{2}-2b^{2}$$

Combine a^{2} and -2a^{2} to get -a^{2}.

$$2x^{2}-24x+72-a^{2}+2ab+b^{2}-2b^{2}$$

Combine b^{2} and -2b^{2} to get -b^{2}.

$$2x^{2}-24x+72-a^{2}+2ab-b^{2}$$

Expand

$$2x^{2}-24x+2ab-a^{2}-b^{2}+72$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-6\right)^{2}.

$$2\left(x^{2}-12x+36\right)+\left(a+b\right)^{2}-2\left(a^{2}+b^{2}\right)$$

Use the distributive property to multiply 2 by x^{2}-12x+36.

$$2x^{2}-24x+72+\left(a+b\right)^{2}-2\left(a^{2}+b^{2}\right)$$

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(a+b\right)^{2}.

$$2x^{2}-24x+72+a^{2}+2ab+b^{2}-2\left(a^{2}+b^{2}\right)$$

Use the distributive property to multiply -2 by a^{2}+b^{2}.

$$2x^{2}-24x+72+a^{2}+2ab+b^{2}-2a^{2}-2b^{2}$$

Combine a^{2} and -2a^{2} to get -a^{2}.

$$2x^{2}-24x+72-a^{2}+2ab+b^{2}-2b^{2}$$

Combine b^{2} and -2b^{2} to get -b^{2}.

$$2x^{2}-24x+72-a^{2}+2ab-b^{2}$$