# How do you find the product (2a+9)(5a-6)?

Apr 23, 2017

$10 {a}^{2} + 33 a - 54$

#### Explanation:

Notice that these are factors.

You can use the FOIL method or the Distributive Property .

What is FOIL ???

FOIL- First Outer Inner Last

$\left(2 a + 9\right) \left(5 a - 6\right)$

First: Multiply the first term in the first factor with the first term in the second factor. NB: both numbers are the first of both factors.

$2 a \times 5 a = 10 {a}^{2}$

Outer: Multipy the first term in the first factor with the last term in the second factor. NB: both numbers are the last of both factors.

$2 a \times - 6 = - 12 a$

Inner: Multiply the last term in the first factor with the first term in the second factor. NB: both numbers are innermost numbers.

$9 \times 5 a = 45 a$

Last: Multiply the last term in the first factor with the last term in the second factor. NB: both numbers are the last numbers of each factor.

$9 \times - 6 = - 54$

$10 {a}^{2} + \left(- 12 a\right) + 45 a + \left(- 54\right)$

$10 {a}^{2} - 12 a + 45 a - 54$

$10 {a}^{2} + 33 a - 54$

What is the Distributive Property ???

The distributive property is simply taking the first term in the first factor and multiplying it by the second term.

$2 a \left(5 a - 6\right) = 10 {a}^{2} - 12 a$

Next, take the second term in the first factor and mutilply it by the second factor.

$9 \left(5 a - 6\right) = 45 a - 54$

$\left(10 {a}^{2} - 12 a\right) + \left(45 a - 54\right)$

$10 {a}^{2} - 12 a + 45 a - 54$

$10 {a}^{2} + 33 a - 54$

I hope this was well explained.

Follow the same steps and try to solve $\left(5 x - 3\right) \left(6 + 8 x\right)$

You should get $40 {x}^{2} + 6 x - 18$ as the answer.

All the best!