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

$$( a + c ) ( a - c ) + b ( b + 2 a )$$

Evaluate

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

Solution Steps

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

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

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

$$a^{2}-c^{2}+b^{2}+2ba$$

Expand

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

Solution Steps

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

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

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

$$a^{2}-c^{2}+b^{2}+2ba$$