Solve 5(2a-1)(a+b)-3(a-3)(a+6)

$$5 ( 2 a - 1 ) ( a + b ) - 3 ( a - 3 ) ( a + 6 )$$

Expand

$$7a^{2}+10ab-14a-5b+54$$

Solution Steps

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

$$\left(10a-5\right)\left(a+b\right)-3\left(a-3\right)\left(a+6\right)$$

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

$$10a^{2}+10ab-5a-5b-3\left(a-3\right)\left(a+6\right)$$

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

$$10a^{2}+10ab-5a-5b+\left(-3a+9\right)\left(a+6\right)$$

Apply the distributive property by multiplying each term of -3a+9 by each term of a+6.

$$10a^{2}+10ab-5a-5b-3a^{2}-18a+9a+54$$

Combine -18a and 9a to get -9a.

$$10a^{2}+10ab-5a-5b-3a^{2}-9a+54$$

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

$$7a^{2}+10ab-5a-5b-9a+54$$

Combine -5a and -9a to get -14a.

$$7a^{2}+10ab-14a-5b+54$$

Evaluate

$$5\left(2a-1\right)\left(a+b\right)-3\left(a-3\right)\left(a+6\right)$$

Solution Steps

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

$$\left(10a-5\right)\left(a+b\right)-3\left(a-3\right)\left(a+6\right)$$

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

$$10a^{2}+10ab-5a-5b-3\left(a-3\right)\left(a+6\right)$$

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

$$10a^{2}+10ab-5a-5b+\left(-3a+9\right)\left(a+6\right)$$

Apply the distributive property by multiplying each term of -3a+9 by each term of a+6.

$$10a^{2}+10ab-5a-5b-3a^{2}-18a+9a+54$$

Combine -18a and 9a to get -9a.

$$10a^{2}+10ab-5a-5b-3a^{2}-9a+54$$

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

$$7a^{2}+10ab-5a-5b-9a+54$$

Combine -5a and -9a to get -14a.

$$7a^{2}+10ab-14a-5b+54$$