How do I factor the expression 4x(squared) + 28xy + 49y(squared)?

Question

I know their is some sort of short cut equation, but I can't remember it.

btw this is for summer school, and I am dangerously close to failing and having to take it again during the second half of summer.

Answer 1

i think you need to use the quadratic formula since none of those numbers have similar variables.

-b +/- square root of b squared - 4ac all divided by 2a

Answer 2

4x2 + 28xy + 49y2
Look at the front and at the back coefficients.
Then look at the middle term coefficient.
Lets see what we can work out here...

Remember Pascals Triangle.
1
11
121 <------
1331
14641
...

28 / 2 = 14 ---> 7 and 2

(2x + 7y)^2

Looks like this works.

BTW,
I don't know that there a specific equation to derive this answer.

Thanks for posting!

Answer 3

You should be able to immediately write down as the answer (2x+7y)^2.

(a+b)^2 = (a^2 +2ab +b^2) should be burned in your memory.
In your problem 4x^2 +28xy +7y^2. Can you see that a = 2x and b= 7y and thus 2ab = 28xy.
Also burned in your memory should be:
(a-b)^2 = a^2-2ab-b^2, and
(a^2-b^2) = (a+b)(a-b).

Answer 4

4x^2 + 28xy +49y^2
=(2x + 7y)^2

Answer 5

4x^2 + 28xy + 49y^2
= (2x + 7y) (2x + 7y)
= (2x + 7y)^2

Answer 6

4x² + 28 xy + 49y
= (2x + 7y).(2x + 7y)
= (2x + 7y)²

Answer 7

you will surely get a calculator here to help you factor this expression at http://www.algebrahelp.com and good luck!

Answer 8

4x^2+28xy+49y^2
=(2x)^2+2.2x.7y+(7y)^2
=(2x+7y)^2----------(a+b)^2=a^2+2ab+b^2

Answer 9

and why do you need to know this?..?..