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

$$( a - b ) ^ { 2 } + ( a - b ) ( a + b )$$

Evaluate

$$2a\left(a-b\right)$$

Solution Steps

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

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

Consider \left(a-b\right)\left(a+b\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

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

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

Combine b^{2} and -b^{2} to get 0.

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

Expand

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

Solution Steps

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

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

Consider \left(a-b\right)\left(a+b\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

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

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

Combine b^{2} and -b^{2} to get 0.

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