Solve {l}{a(a-3b)}{+(a+b)^2}{-a(a-b)}

$$\left. \begin{array} { l } { a ( a - 3 b ) } \\ { + ( a + b ) ^ { 2 } } \\ { - a ( a - b ) } \end{array} \right.$$

Evaluate

$$a^{2}+b^{2}$$

Solution Steps

Use the distributive property to multiply a by a-3b.

$$a^{2}-3ab+\left(a+b\right)^{2}-a\left(a-b\right)$$

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

$$a^{2}-3ab+a^{2}+2ab+b^{2}-a\left(a-b\right)$$

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

$$2a^{2}-3ab+2ab+b^{2}-a\left(a-b\right)$$

Combine -3ab and 2ab to get -ab.

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

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

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

To find the opposite of a^{2}-ab, find the opposite of each term.

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

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

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

Combine -ab and ab to get 0.

$$a^{2}+b^{2}$$

Expand

$$a^{2}+b^{2}$$

Solution Steps

Use the distributive property to multiply a by a-3b.

$$a^{2}-3ab+\left(a+b\right)^{2}-a\left(a-b\right)$$

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

$$a^{2}-3ab+a^{2}+2ab+b^{2}-a\left(a-b\right)$$

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

$$2a^{2}-3ab+2ab+b^{2}-a\left(a-b\right)$$

Combine -3ab and 2ab to get -ab.

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

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

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

To find the opposite of a^{2}-ab, find the opposite of each term.

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

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

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

Combine -ab and ab to get 0.

$$a^{2}+b^{2}$$