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

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Solution

(a+b)3=[(a+b)(a+b)] (a+b)=[a2+b2+2ab](a+b)

a(a2+b2+2ab)+b(a2+b2+2ab)

=a3+ab2+2(a2)b+(a2)b+b3+2a(b2)=a3+3a2b+3ab2+b3 = l.h.s

HENCE VERIFIED!.

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Similar questions

a^{3}

–

b^{3}

(a - b)^{3}

+ 3ab(a - b)

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)

Q. Verify:

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

for

a = 3, b = 4

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

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

Which of the following is an expansion of the identity ${(a - b)}^{3}$ ?

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

(a+b)3=[(a+b)(a+b)] (a+b)=[a2+b2+2ab](a+b) a(a2+b2+2ab)+b(a2+b2+2ab) =a3+ab2+2(a2)b+(a2)b+b3+2a(b2)=a3+3a2b+3ab2+b3 = l.h.s HENCE VERIFIED!.

(a+b)3=[(a+b)(a+b)] (a+b)=[a2+b2+2ab](a+b)

a(a2+b2+2ab)+b(a2+b2+2ab)

=a3+ab2+2(a2)b+(a2)b+b3+2a(b2)=a3+3a2b+3ab2+b3 = l.h.s

HENCE VERIFIED!.