Which of the following is correct?

MCQ

A
$(a - b)^2 = a^2 + 2ab - b^2$
✓
$(a - b)^2= a^2 - 2ab + b^2$
C
$(a - b)^2 = a^2- b^2$
D
$(a + b)^2 = a^2 + 2ab - b^2$

✓

Answer

Correct option: B.

$(a - b)^2= a^2 - 2ab + b^2$

B. $(a - b)^2= a^2 - 2ab + b^2$
Solution:
$(a-b)^2=(a-b)(a-b) $
$ =a(a-b)-b(a-b) $
$ =a \cdot a-a \cdot b-b \cdot a+b \cdot b $
$ =a^2-a b-a b+b^2 $
$ =a^2-2 a b+b^2 \&(a+b)^2$
$ =(a+b)(a+b) $
$ =a \cdot a+a \cdot b+b \cdot a+b \cdot b $
$ =a^2+2 a b+b^2$

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