Question 6
Write the following cubes in expanded form:

$(i) (2 x + 1)^{3} (i i) (2 a - 3 b)^{3} (i i i) {[\frac{3}{2} x + 1]}^{3} (i v) {[x - \frac{2}{3} y]}^{3}$

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Solution

$(i) (2 x + 1)^{3} U s i n g i d e n t i t y (a + b)^{3} = a^{3} + b^{3} + 3 a b (a + b) = (2 x)^{3} + 1^{3} + 3 (2 x) (1) (2 x + 1) = 8 x^{3} + 1 + 6 x (2 x + 1) = 8 x^{3} + 12 x^{2} + 6 x + 1$

$(i i) (2 a - 3 b)^{3} U s i n g i d e n t i t y (a - b)^{3} = a^{3} - b^{3} - 3 a b (a - b) = (2 a)^{3} - (3 b)^{3} - 3 \times 2 a \times 3 b (2 a - 3 b) = 8 a^{3} - 27 b^{3} - 18 a b (2 a - 3 b) = 8 a^{3} - 27 b^{3} - 36 a^{2} b + 54 a b^{2}$

$(i i i) {[\frac{3}{2} x + 1]}^{3} U s i n g i d e n t i t y (a + b)^{3} = a^{3} + b^{3} + 3 a b (a + b) = {(\frac{3}{2} x)}^{3} + 1^{3} + 3 (\frac{3}{2} x) (1) (\frac{3}{2} x + 1) = \frac{27}{8} x^{3} + 1 + \frac{9}{2} x (\frac{3}{2} x + 1) = \frac{27}{8} x^{3} + \frac{27}{4} x^{2} + \frac{9}{2} x + 1$

$(i v) {[x - \frac{2}{3} y]}^{3} U s i n g i d e n t i t y (a - b)^{3} = a^{3} - b^{3} - 3 a b (a - b) = x^{3} - {(\frac{3}{2} y)}^{3} - 3 (x) (\frac{2}{3} y) (x - \frac{2}{3} y) = x^{3} - \frac{8}{27} y^{3} - 2 x y (x - \frac{2}{3} y) = x^{3} - \frac{8}{27} y^{3} - 2 x^{2} y + \frac{4}{3} x y^{2}$

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Similar questions

Write the following cubes in expanded form:

(i) $(2 x + 1)^{3}$

(ii) $(2 a - 3 b)^{3}$

(iii) $(\frac{3}{2} x + 1)^{3}$

(iv) $(x - \frac{2}{3} y)^{3}$

Write the following cubes in expanded form:
(i) ${(2 x + 1)}^{3}$
(ii) ${(2 a - 3 b)}^{3}$

Write the following cubes in expanded form:
$(i) (2 x + 1)^{3}$
$(i i) (2 a - 3 b)^{3}$
$(i i i) {[\frac{3}{2} x + 1]}^{3}$
$(i v) {[x - \frac{2}{3} y]}^{3}$

Q. Write the following cubes in expanded from:
(i)

(2 x + 1)^{3}

(ii)

(2 a - 3 b)^{3}

(iii)

{[\frac{3}{2} x + 1]}^{3}

(iv)

{[x - \frac{2}{3} y]}^{3}

Q. Write the following in the expanded form:

(i) (a +2b + c)²

(ii) (2a − 3b − c)²

(iii) (−3x + y + z)²

(iv) (m + 2n − 5p)²

(v) (2 + x − 2y)²

(vi) (a² + b² + c²)²

(vii) (ab + bc + ca)²

(viii)

{(\frac{x}{y} + \frac{y}{z} + \frac{z}{x})}^{2}

(ix)

{(\frac{a}{b c} + \frac{b}{c a} + \frac{c}{a b})}^{2}

(x)

(x + 2 y + 4 z)^{2}

(xi) (2x − y + z)²

(xii) (−2x + 3y + 2z)²

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Standard IX Mathematics

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Question 6 Write the following cubes in expanded form: (i) (2x+1)3(ii) (2a−3b)3(iii)[32x+1]3(iv)[x−23y]3

Question 6
Write the following cubes in expanded form:

$(i) (2 x + 1)^{3} (i i) (2 a - 3 b)^{3} (i i i) {[\frac{3}{2} x + 1]}^{3} (i v) {[x - \frac{2}{3} y]}^{3}$