The correct option is B True(a b)^3 = a^3 b^3 3ab(a b) Hence, a^3 – b^3 = (a b)^3 + 3ab(a b) ...

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Byju's Answer

Standard VIII

Mathematics

Cube Numbers

a3-b3=a-b3+3 ...

Question

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

True

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False

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Solution

The correct option is A True
$(a - b)^{3} = a^{3} - b^{3} - 3 a b (a - b)$
Hence, $a^{3}$ – $b^{3}$ = $(a - b)^{3}$ + 3ab(a - b)

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Similar questions

Q. Verify:

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

for

a = 3, b = 4

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?

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

Can you tell me the derivation of identity (a + b)3 = a3 + b3 + 3ab (a + b)

Find the number of dissimilar terms in the expansion of $(a^{3} + b^{3} + 3 a b (a + b))^{50}$

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a3 – b3 = (a−b)3 + 3ab(a - b)​

The correct option is A True(a−b)3=a3−b3−3ab(a−b) Hence, a3 – b3 = (a−b)3 + 3ab(a - b)​

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

The correct option is A True
$(a - b)^{3} = a^{3} - b^{3} - 3 a b (a - b)$
Hence, $a^{3}$ – $b^{3}$ = $(a - b)^{3}$ + 3ab(a - b)