Question

Which of the following equations are correct?

$\left(i\right)(a+b+c{)}^2=a^2+b^2+c^2-2(ab+bc+ca)$
$\left(ii\right)(a+b{)}^3=a^3+b^3+3ab(a-b)$
$\left(iii\right)(a-b{)}^3=a^3-b^3-3ab(a+b)$
$\left(iv\right)a^2-b^2=(a+b)(a-b)$

• A. (iv) only
• B. (i) and (iv)
• C. (iv) and (iii)
• D. (ii), (iii) and (iv)

Answer 1

The correct option is A

(iv) only

Using identities
$(a+b+c{)}^2=a^2+b^2+c^2+2(ab+bc+ca)$
$(a+b{)}^3=a^3+b^3+3ab(a+b)$
$(a-b{)}^3=a^3-b^3-3ab(a-b)$
$a^2-b^2=(a+b)(a-b)$