# Factored form to standard form (2x+y)(2x-y)

jeew-m | Certified Educator

calendarEducator since 2012

starTop subjects are Math, Science, and Social Sciences

Let take;

`A = 2x`

`B = y`

Now the question will look like;

`(2x+y)(2x-y)`

`= (A+B)(A-B)`

Now multiply first bold part in bracket 1 which is A with the other bracket in italic which is (A-B). Then do the same for B in the first bracket and add the two.

`(A+B)(A-B)`

`= A(A-B)+B(A-B)`

`= A*A-A*B+B*A-B*B`

`= A^2-AB+AB-B^2`       notice that AB term cancels.

`= A^2-B^2`

So we got;

(A+B)(A-B) = A^2-B^2

Put the real values of A and B;

`(A+B)(A-B) = A^2-B^2`

`(2x+y)(2x-y) = (2x)^2-y^2`

`(2x+y)(2x-y) = 4x^2-y^2`

So the answer is ` (2x+y)(2x-y) = 4x^2-y^2`

check Approved by eNotes Editorial

mathsworkmusic | Certified Educator

calendarEducator since 2012

starTop subjects are Math, Science, and Business

Multiply the first term in the first bracket with the first and second terms in the second bracket, and then the second term in the second bracket with the first and second terms in the second bracket. Gather terms in x, xy and y.

4x^2 + 2x*(-y) + y*(2x)+y*(-y) = 4x^2-2xy+2xy-y^2 = 4x^2-y^2

check Approved by eNotes Editorial