The correct options are A (a+b)(a^2+b^2 ab) B (a+b)^3 3ab(a+b) We know that (a+b)^3=a^3+b^3+3ab(a+b) ⇒ a^3+b^3=(a+b)^3 3ab(a+b) ... (i) ⇒ a^3+b^3=(a+b)^3 3ab(a ...

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Identity (a^3+b^3)

a3+b3=

Question

$a^{3} + b^{3} =$

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

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$(a + b)^{3} - 3 a b (a + b)$

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$(a + b)^{3} + 3 a b (a + b)$

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

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Solution

The correct options are
A
$(a + b) (a^{2} + b^{2} - a b)$

B
$(a + b)^{3} - 3 a b (a + b)$

We know that $(a + b)^{3} = a^{3} + b^{3} + 3 a b (a + b)$

$\Rightarrow a^{3} + b^{3} = (a + b)^{3} - 3 a b (a + b)$ ... (i)

$\Rightarrow a^{3} + b^{3} = (a + b)^{3} - 3 a b (a + b) = (a + b) [(a + b)^{2} - 3 a b]$

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

$= (a + b) (a^{2} + b^{2} - a b)$ ... (ii)

Suggest Corrections

Similar questions

Q. 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)

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

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

Q. The product (a + b) (a − b) (a² − ab + b²) (a² + ab + b²) is equal to

(a) a⁶ + b⁶

(b) a⁶ − b⁶

(c) a³ − b³

(d) a³+ b³

a^{3}

–

b^{3}

(a - b)^{3}

+ 3ab(a - b)

State the following statement is True or False:

a^{3} - b^{3} = (a - b) (a^{2} + b^{2} + a b)

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a3+b3=

The correct options are A (a+b)(a2+b2−ab) B (a+b)3−3ab(a+b) We know that (a+b)3=a3+b3+3ab(a+b) ⇒a3+b3=(a+b)3−3ab(a+b) ... (i) ⇒a3+b3=(a+b)3−3ab(a+b)=(a+b)[(a+b)2−3ab] =(a+b)(a2+b2+2ab−3ab) =(a+b)(a2+b2−ab) ... (ii)

$a^{3} + b^{3} =$