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

1 Answer
Apr 23, 2017

Answer:

#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!