Which of the following equations are correct?

$(i) (a + b + c)^{2} = a^{2} + b^{2} + c^{2} - 2 (a b + b c + c a)$
$(i i) (a + b)^{3} = a^{3} + b^{3} + 3 a b (a - b)$
$(i i i) (a - b)^{3} = a^{3} - b^{3} - 3 a b (a + b)$
$(i v) a^{2} - b^{2} = (a + b) (a - b)$

(iv) and (iii)

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(i) and (iv)

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(iv) only

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(ii), (iii) and (iv)

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Solution

The correct option is C
(iv) only

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

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Similar questions

Which of the following equation/s is/are correct?

$i) (a + b + c)^{2} = a^{2} + b^{2} + c^{2} - 2 (a b + b c + c a)$
$i i) (a + b)^{3} = a^{3} + b^{3} + 3 a b (a - b)$
$i i i) (a - b)^{3} = a^{3} - b^{3} - 3 a b (a + b)$
$i v) a^{2} - b^{2} = (a + b) (a - b)$

Find $\frac{(a^{2} - b^{2})^{3} + (b^{2} - c^{2})^{3} + (c^{2} - a^{2})^{3}}{(a - b)^{3} + (b - c)^{3} + (c - a)^{3}} =$

a^{3}

–

b^{3}

(a - b)^{3}

+ 3ab(a - b)

Expand the following formulas

(a + b)^{2}

(a - b)^{2}

(a^{2} + b^{2})

(a + b)^{3}

(a - b)^{3}

a^{3} + b^{3}

a^{3} - b^{3}

Q. Simplify:

\frac{(a^{2} - b^{2}) + {(b^{2} - c^{2})}^{3} + {(c^{2} - a^{2})}^{3}}{{(a - b)}^{3} + {(b - c)}^{3} + {(c - a)}^{3}}

Which of the following equations are correct? (i) (a+b+c)2=a2+b2+c2−2(ab+bc+ca) (ii) (a+b)3=a3+b3+3ab(a−b) (iii) (a−b)3=a3−b3−3ab(a+b) (iv) a2−b2=(a+b)(a−b)

The correct option is C (iv) only Using identities (a+b+c)2=a2+b2+c2+2(ab+bc+ca) (a+b)3=a3+b3+3ab(a+b) (a−b)3=a3−b3−3ab(a−b) a2−b2=(a+b)(a−b)

Which of the following equations are correct?

$(i) (a + b + c)^{2} = a^{2} + b^{2} + c^{2} - 2 (a b + b c + c a)$
$(i i) (a + b)^{3} = a^{3} + b^{3} + 3 a b (a - b)$
$(i i i) (a - b)^{3} = a^{3} - b^{3} - 3 a b (a + b)$
$(i v) a^{2} - b^{2} = (a + b) (a - b)$

The correct option is C
(iv) only

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