simplify (5+11) (5x-11)

Question

simplify (5+11) (5x-11) make the equation smaller

Answer 1

Wow some make this to difficult.  Assuming its written correctly, Noemi S. has it dead on.

 (5+11)(5x-11)=

16(5x-11)=

80x-176

Keep it simple!

Answer 2

(5+11)(5x-11)= 16(5x-11)= 80x-176

 

Answer 3

The question is misleading because the student might get confused with a similar problem that they get wrong in the future because (5+11) can be as easily mathematically written as 16(5x-11). This is important for those that learn mathematical operations by application of visual/spatial pattern recognition and then step work. While the idea is to train them to think in a mathematical - logical framework and to look closely to details (i.e., left brain functions), it is possible to train both students to be equally effective when the other uses right brain big picture function combined with the left brain love for pattern recognition.

Answer 4

I would ask if is it an expression or is something left out.  Then I would answer the question.

 

Answer 5

My assumption is that the problem stands as is and there is no mistake except for the statement this is an equation.  

Thus to simplify:

(5 + 11)(5x + -11)

Combine the terms withing the first Parenthesis: 5 + 11 = 16
(16)(5x + -11)

Reorder the terms although not necessary in this order.
16(-11 + 5x)
(-11 * 16 + 5x * 16)

Thus.. (-176 + 80x) or (80x + -176) or (80x - 176)

I think it is easier to understand if you do not think in terms of addition and subtraction, but always in terms of adding positive and negative numbers.  

have fun..

 

Answer 6

I am also going to make the assumption that the original problem was simplifying (5x + 11)(5x - 11)

Just in case it is a little unclear as to why exactly something of the form (a + b)(a - b) = (a^2 - b^2) I'm going to use the foil method to show the same thing many people already have.

So we have

(5x + 11)(5x - 11)

Hopefully you have heard of FOIL which stands for First, Outer, Inner, Last, and refers to which parts of the factored problem should be multiplied.

First: 5x, 5x

Outer: 5x, -11

Inner: 11, 5x

Last: 11, -11

Let's multiply each pairing together and then add each product together so we get:

25x^2 - 55x + 55x - 121

in the middle we can see that -55x + 55x is trivial and equals zero so:

25x^2 + 0 - 121

and finally

25x^2 - 121

As many people have been pointing out though, the form which the original problem is in should tip you off that you are in for a "difference of squares." This will always happen because the form that it is in, namely (a + b)(a - b) it will always be the case that when expanded the "Outer" multiplication will cancel out the "Inner" multiplication, so using FOIL will end up taking longer than necessary.

Hope that helps!

Answer 7

Hi Ariana!

I think you may have left out an "x".
Did you mean (5x + 11)(5x - 11)?
If so, this is the factored form of the "difference of two squares".
This is a common form that you will see many times, almost certainly on a test somewhere. Be on the lookout for it because it makes simple work of what would otherwise be a more difficult solution.

The form is like this:
(a^2 - b^2) = (a + b)(a - b)
a would be 5x, and b would be 11, so:
((5x)^2 - 11^2) = (5x + 11)(5x - 11)
25x^2 - 121 = (5x + 11)(5x - 11)

-------

As you wrote it above, it would be a trivial process to simplify it:

(5 + 11)(5x - 11)
(16)(5x - 11)
80x - 176

Hope this helps!
Gene G.

Answer 8

I am assuming that you meant (5x + 11)(5x -11).

Difference of squares states (a + b)(a - b) = a² - b².

In the case of this problem, a = 5x and b = 11

(5x)² - 11²

25x² - 121

If the problem is (5 + 11)(5x - 11) as you wrote it, then you just need to add 5 and 11, then distribute

(5 + 11)(5x - 11)

16(5x - 11)

80x - 176