Solve (a+b)^2-2(a+b)+1quadx^2

$$( a + b ) ^ { 2 } - 2 ( a + b ) + 1 \quad x ^ { 2 }$$

Evaluate

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

Solution Steps

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

$$a^{2}+2ab+b^{2}-2\left(a+b\right)+1x^{2}$$

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

$$a^{2}+2ab+b^{2}-2a-2b+1x^{2}$$

For any term t, t\times 1=t and 1t=t.

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

Expand

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

Solution Steps

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

$$a^{2}+2ab+b^{2}-2\left(a+b\right)+1x^{2}$$

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

$$a^{2}+2ab+b^{2}-2a-2b+1x^{2}$$

For any term t, t\times 1=t and 1t=t.

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