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

$$( a + b ) ( a - b ) - a ( 2 a - 1 )$$

Evaluate

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

Solution Steps

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}.

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

Use the distributive property to multiply a by 2a-1.

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

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

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

The opposite of -a is a.

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

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

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

Expand

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

Solution Steps

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}.

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

Use the distributive property to multiply a by 2a-1.

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

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

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

The opposite of -a is a.

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

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

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