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

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jeew-m's profile pic

jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted on

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`

 

 

 

 

mathsworkmusic's profile pic

mathsworkmusic | (Level 2) Educator

Posted on

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

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