Solve 5(2a-1)(a+b)-3(a-3)(a+b)

$$5 ( 2 a - 1 ) ( a + b ) - 3 ( a - 3 ) ( a + b )$$

Evaluate

$$\left(7a+4\right)\left(a+b\right)$$

Solution Steps

Use the distributive property to multiply 5 by 2a-1.

$$\left(10a-5\right)\left(a+b\right)-3\left(a-3\right)\left(a+b\right)$$

Apply the distributive property by multiplying each term of 10a-5 by each term of a+b.

$$10a^{2}+10ab-5a-5b-3\left(a-3\right)\left(a+b\right)$$

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

$$10a^{2}+10ab-5a-5b+\left(-3a+9\right)\left(a+b\right)$$

Apply the distributive property by multiplying each term of -3a+9 by each term of a+b.

$$10a^{2}+10ab-5a-5b-3a^{2}-3ab+9a+9b$$

Combine 10a^{2} and -3a^{2} to get 7a^{2}.

$$7a^{2}+10ab-5a-5b-3ab+9a+9b$$

Combine 10ab and -3ab to get 7ab.

$$7a^{2}+7ab-5a-5b+9a+9b$$

Combine -5a and 9a to get 4a.

$$7a^{2}+7ab+4a-5b+9b$$

Combine -5b and 9b to get 4b.

$$7a^{2}+7ab+4a+4b$$

Expand

$$7a^{2}+7ab+4a+4b$$

Solution Steps

Use the distributive property to multiply 5 by 2a-1.

$$\left(10a-5\right)\left(a+b\right)-3\left(a-3\right)\left(a+b\right)$$

Apply the distributive property by multiplying each term of 10a-5 by each term of a+b.

$$10a^{2}+10ab-5a-5b-3\left(a-3\right)\left(a+b\right)$$

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

$$10a^{2}+10ab-5a-5b+\left(-3a+9\right)\left(a+b\right)$$

Apply the distributive property by multiplying each term of -3a+9 by each term of a+b.

$$10a^{2}+10ab-5a-5b-3a^{2}-3ab+9a+9b$$

Combine 10a^{2} and -3a^{2} to get 7a^{2}.

$$7a^{2}+10ab-5a-5b-3ab+9a+9b$$

Combine 10ab and -3ab to get 7ab.

$$7a^{2}+7ab-5a-5b+9a+9b$$

Combine -5a and 9a to get 4a.

$$7a^{2}+7ab+4a-5b+9b$$

Combine -5b and 9b to get 4b.

$$7a^{2}+7ab+4a+4b$$