Factorise a-2 b-a3-8 b3A- a-2 ba2-2 a b-b2B- a-2 ba2-2 a b-b2-1C- a -2 b a 2-2 ab - b 2-1D- a-2 ba2-2 a b-b2-2

The correct option is B (a+2b) (a^2 2ab+b^2 + 1) Given a+2b + a^3 +8b^3 →a+2b + (a)^3 +(2b)^3 →(a+2b) + (a+2b)(a^2 2ab+b^2) (Using (a^3+b^3 ...

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Byju's Answer

Standard IX

Mathematics

Factorisation Using Algebraic Identities

Factorise a+2...

Question

Factorise $a + 2 b + a^{3} + 8 b^{3}$

$(a + 2 b) (a^{2} - 2 a b + b^{2} - 1)$

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$(a + 2 b) (a^{2} - 2 a b + b^{2} + 1)$

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

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

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Solution

The correct option is B
$(a + 2 b) (a^{2} - 2 a b + b^{2} + 1)$

Given
$a + 2 b + a^{3} + 8 b^{3}$

$\to$ $a + 2 b + (a)^{3} + (2 b)^{3}$

$\to$ $(a + 2 b) + (a + 2 b) (a^{2} - 2 a b + b^{2})$ ( $U s i n g (a^{3} + b^{3})$
Taking $a + 2 b$ common ,we have
$\to$ $(a + 2 b) (a^{2} - 2 a b + b^{2} + 1)$

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Similar questions

Q. Question 3

Which of the following is correct?
a)

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

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

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

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

Which of the following is correct?
a) $(a - b)^{2} = a^{2} + 2 a b - b^{2}$
b) $(a - b)^{2} = a^{2} - 2 a b + b^{2}$
c) $(a - b)^{2} = a^{2} - b^{2}$
d) $(a + b)^{2} = a^{2} + 2 a b - b^{2}$

Q. The expansion for the identity

{(a - b)}^{2}

is .

Q. Simplify:
(a² + b² + 2ab) − (a² + b² −2ab)

Q. Evaluate:

\sqrt{\frac{a^{2} + 2 a b + b^{2}}{a^{2} - 2 a b + b^{2}}}

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Factorise a+2b+a3+8b3

The correct option is B (a+2b)(a2−2ab+b2+1) Given a+2b+a3+8b3 →a+2b+(a)3+(2b)3 →(a+2b)+(a+2b)(a2−2ab+b2) (Using(a3+b3) Taking a+2b common ,we have →(a+2b)(a2−2ab+b2+1)

Factorise $a + 2 b + a^{3} + 8 b^{3}$