Verify:
$a^{3} + b^{3} = (a + b)^{3} - 3 a b (a + b)$ for $a = 3, b = 4$ .

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Solution

For $a = 3, b = 4$ we have,
$a^{3} + b^{3} = 3^{3} + 4^{3} = 27 + 64 = 91$ ……… $(1)$
Now, $(a + b)^{3} - 3 a b (a + b)$
$= 7^{3} - 3.3.4.7$
$= 7 (49 - 36) = 7.13 = 91$ ……… $(2)$
From $(1)$ & $(2)$ it is clean that,
$(a^{3} + b^{3}) = (a + b)^{3} - 3 a b (a + b)$ is true for $a = 3, b = 4$ .

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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)

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)

Q. Verify:

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

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Verify:a3+b3=(a+b)3−3ab(a+b) for a=3,b=4.

For a=3,b=4 we have,a3+b3=33+43=27+64=91 ………(1)Now, (a+b)3−3ab(a+b)=73−3.3.4.7=7(49−36)=7.13=91 ………(2)From (1) & (2) it is clean that,(a3+b3)=(a+b)3−3ab(a+b) is true for a=3,b=4.

Verify:
$a^{3} + b^{3} = (a + b)^{3} - 3 a b (a + b)$ for $a = 3, b = 4$ .