Solve (a-2b)(a+2b)-(a-2b)+8b^2

$$( a - 2 b ) ( a + 2 b ) - ( a - 2 b ) + 8 b ^ { 2 }$$

Evaluate

$$a^{2}-a+4b^{2}+2b$$

Solution Steps

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

$$a^{2}-\left(2b\right)^{2}-\left(a-2b\right)+8b^{2}$$

Expand \left(2b\right)^{2}.

$$a^{2}-2^{2}b^{2}-\left(a-2b\right)+8b^{2}$$

Calculate 2 to the power of 2 and get 4.

$$a^{2}-4b^{2}-\left(a-2b\right)+8b^{2}$$

To find the opposite of a-2b, find the opposite of each term.

$$a^{2}-4b^{2}-a+2b+8b^{2}$$

Combine -4b^{2} and 8b^{2} to get 4b^{2}.

$$a^{2}+4b^{2}-a+2b$$

Expand

$$a^{2}-a+4b^{2}+2b$$

Solution Steps

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

$$a^{2}-\left(2b\right)^{2}-\left(a-2b\right)+8b^{2}$$

Expand \left(2b\right)^{2}.

$$a^{2}-2^{2}b^{2}-\left(a-2b\right)+8b^{2}$$

Calculate 2 to the power of 2 and get 4.

$$a^{2}-4b^{2}-\left(a-2b\right)+8b^{2}$$

To find the opposite of a-2b, find the opposite of each term.

$$a^{2}-4b^{2}-a+2b+8b^{2}$$

Combine -4b^{2} and 8b^{2} to get 4b^{2}.

$$a^{2}+4b^{2}-a+2b$$