Question

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

Answer 1

`10a^2+33a-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

`(2a+9)(5a-6)`

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.

`2axx5a=10a^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.

`2axx-6=-12a`

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

`9xx5a=45a`

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.

`9xx-6=-54`

Now add the numbers.

`10a^2+(-12a)+45a+(-54)`

`10a^2-12a+45a-54`

`10a^2+33a-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.

`2a(5a-6)=10a^2-12a`

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

`9(5a-6)=45a-54`

Add the products

`(10a^2-12a)+(45a-54)`

`10a^2-12a+45a-54`

`10a^2+33a-54`

I hope this was well explained.

Follow the same steps and try to solve `(5x-3)(6+8x)`

You should get `40x^2+6x-18` as the answer.

All the best!