Solve (a(a-3b)+(a-b)(a+3b)

$$( a ( a - 3 b ) + ( a - b ) ( a + 3 b )$$

Evaluate

$$\left(2a-3b\right)\left(a+b\right)$$

Solution Steps

Use the distributive property to multiply a by a-3b.

$$a^{2}-3ab+\left(a-b\right)\left(a+3b\right)$$

Apply the distributive property by multiplying each term of a-b by each term of a+3b.

$$a^{2}-3ab+a^{2}+3ab-ba-3b^{2}$$

Combine 3ab and -ba to get 2ab.

$$a^{2}-3ab+a^{2}+2ab-3b^{2}$$

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

$$2a^{2}-3ab+2ab-3b^{2}$$

Combine -3ab and 2ab to get -ab.

$$2a^{2}-ab-3b^{2}$$

Expand

$$2a^{2}-ab-3b^{2}$$

Solution Steps

Use the distributive property to multiply a by a-3b.

$$a^{2}-3ab+\left(a-b\right)\left(a+3b\right)$$

Apply the distributive property by multiplying each term of a-b by each term of a+3b.

$$a^{2}-3ab+a^{2}+3ab-ba-3b^{2}$$

Combine 3ab and -ba to get 2ab.

$$a^{2}-3ab+a^{2}+2ab-3b^{2}$$

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

$$2a^{2}-3ab+2ab-3b^{2}$$

Combine -3ab and 2ab to get -ab.

$$2a^{2}-ab-3b^{2}$$