Question

(a + b-c+d)2 – (a-b+c-d)2 = ?
Ans
. 4a(b + d -c)
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Answer 1

Answer:

(a + b - c + d)2-(a - b+ c - d) 2

2a+2b-2c+2d-2a-2b+2c-2d

0

Answer 2

We are being given the difference of square

To simplify, use identity $A^2-B^2=(A+B)(A-B)$

Here $A=a+b-c+d$ and $B=a-b+c-d$

$(A+B)(A-B)=\{(a+b-c+d)+(a-b+c-d)\}\{(a+b-c+d)-(a-b+c-d)\}$

$=(a+a+b-b-c+c+d-d)(a-a+b+b-c-c+d+d)$

$=(2a)(2b-2c+2d)$

$=4a(b-c+d)$

Isn't that cool... That's why I love factorization