Solve (a-3b)(a+2b)+5a(a+2b)

$$( a - 3 b ) ( a + 2 b ) + 5 a ( a + 2 b )$$

Evaluate

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

Solution Steps

Apply the distributive property by multiplying each term of a-3b by each term of a+2b.

$$a^{2}+2ab-3ba-6b^{2}+5a\left(a+2b\right)$$

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

$$a^{2}-ab-6b^{2}+5a\left(a+2b\right)$$

Use the distributive property to multiply 5a by a+2b.

$$a^{2}-ab-6b^{2}+5a^{2}+10ab$$

Combine a^{2} and 5a^{2} to get 6a^{2}.

$$6a^{2}-ab-6b^{2}+10ab$$

Combine -ab and 10ab to get 9ab.

$$6a^{2}+9ab-6b^{2}$$

Expand

$$6a^{2}+9ab-6b^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of a-3b by each term of a+2b.

$$a^{2}+2ab-3ba-6b^{2}+5a\left(a+2b\right)$$

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

$$a^{2}-ab-6b^{2}+5a\left(a+2b\right)$$

Use the distributive property to multiply 5a by a+2b.

$$a^{2}-ab-6b^{2}+5a^{2}+10ab$$

Combine a^{2} and 5a^{2} to get 6a^{2}.

$$6a^{2}-ab-6b^{2}+10ab$$

Combine -ab and 10ab to get 9ab.

$$6a^{2}+9ab-6b^{2}$$