Factorize completely; (4x+3y)\(^2\) - (3x-2y)\(^2\)
(x+5y)(7x+y)
(x+5y)(7x-y)
(x-5y)(7x+y)
(x-5y)(7x-y)
Explanation
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The Answer is Option A: (x+5y)(7x-y)
Explanation:
(4x + 3y) ^2 - (3x - 2y)^2
First lets simplify the first bracket *()*:
(4x + 3y) (4x + 3y) = (16x^2 + 12xy + 12xy + 9y^2)
= (16x^2 + 9y^2 + 24xy)
Simplify the Next Bracket *()*
(3x - 2y) (3x - 2y) = (9x^2 - 6xy - 6xy + 4y^2)
= (9x^2 + 4y^2 - 12xy)
Now we Subtract both of them according to the question: (4x + 3y) ^2 - (3x - 2y)^2
= (16x^2 + 9y^2 + 24xy) - (9x^2 + 4y^2 - 12xy)
next we multipy the second bracket by the subtraction "-" sign to open it
So we will have
16x^2 + 9y^2 + 24xy - (9x^2 + 4y^2 - 12xy) = 16x^2 + 9y^2 + 24xy - 9x^2 - 4y^2 + 12xy
So we arrange them accordingly;
16x^2 - 9x^2 + 9y^2 - 4y^2 + 24xy + 12xy
=7x^2+ 5y^2 + 36xy
Option A:
(x + 5y) (7x + y)
7x^2 + xy + 35xy + 5y^2
= 7x^2 + 36xy + 5y2
