The factors of 27 m 3-216 n 3 areA- 3 m -6 n 9 m 2-18 mn -36 n 2-B- 3 m -6 n 9 m 2-18 mn -36 n 2-C- 3 m -6 n 9 m 2-18 mn -36 n 2-D- 3 m -6 n 9 m 2-18 mn -36 n 2-

The correct option is A nbsp; (3m +6n)((9m^2 18mn + 36n^2)Given nbsp; 27m^3 + 216n^3 = nbsp;(3m)^3 + (6n)^3 We know that nbsp; a^3 + b^3 = (a + b)(a ...

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Byju's Answer

Standard VIII

Mathematics

Rational Algebraic Expression

The factors o...

Question

The factors of $27 m^{3} + 216 n^{3}$ are ______________.

(3 m + 6 n) ((9 m^{2} - 18 m n + 36 n^{2})

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(3 m - 6 n) ((9 m^{2} - 18 m n + 36 n^{2})

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(3 m - 6 n) ((9 m^{2} + 18 m n + 36 n^{2})

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(3 m - 6 n) ((9 m^{2} - 18 m n - 36 n^{2})

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Solution

The correct option is A $(3 m + 6 n) ((9 m^{2} - 18 m n + 36 n^{2})$
Given $27 m^{3} + 216 n^{3}$ = $(3 m)^{3} + (6 n)^{3}$
We know that $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$
Here, the given question is of the form $a^{3} + b^{3}$ , where $a = 3 m$ and $b = 6 n$ .
$∴$ $(3 m)^{3} + (6 n)^{3} = (3 m + 6 n) ((3 m)^{2} - 3 m (6 n) + (6 n)^{2})$
$= (3 m + 6 n) ((9 m^{2} - 18 m n + 36 n^{2})$

Suggest Corrections

The factors of 27m3+216n3 are ______________.

The correct option is A (3m+6n)((9m2−18mn+36n2)Given 27m3+216n3 = (3m)3+(6n)3 We know that a3+b3=(a+b)(a2−ab+b2) Here, the given question is of the form a3+b3, where a=3m and b=6n. ∴(3m)3+(6n)3=(3m+6n)((3m)2−3m(6n)+(6n)2) =(3m+6n)((9m2−18mn+36n2)

The factors of $27 m^{3} + 216 n^{3}$ are ______________.