Solve (3+a)(3-a)-a(a-1)

$$( 3 + a ) ( 3 - a ) - a ( a - 1 )$$

Evaluate

$$9+a-2a^{2}$$

Solution Steps

Consider \left(3+a\right)\left(3-a\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$3^{2}-a^{2}-a\left(a-1\right)$$

Calculate 3 to the power of 2 and get 9.

$$9-a^{2}-a\left(a-1\right)$$

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

$$9-a^{2}-\left(a^{2}-a\right)$$

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

$$9-a^{2}-a^{2}-\left(-a\right)$$

The opposite of -a is a.

$$9-a^{2}-a^{2}+a$$

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

$$9-2a^{2}+a$$

Expand

$$9+a-2a^{2}$$

Solution Steps

Consider \left(3+a\right)\left(3-a\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$3^{2}-a^{2}-a\left(a-1\right)$$

Calculate 3 to the power of 2 and get 9.

$$9-a^{2}-a\left(a-1\right)$$

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

$$9-a^{2}-\left(a^{2}-a\right)$$

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

$$9-a^{2}-a^{2}-\left(-a\right)$$

The opposite of -a is a.

$$9-a^{2}-a^{2}+a$$

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

$$9-2a^{2}+a$$