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If x = 2a - 1, y = 2a - 2, z = 3 - 4a, then value of \( \Large x^{3}+y^{3}+z^{3} \) will be

A) \( \Large 6 \left(3-13a+18a^{2}-8a^{3}\right) \)
B) \( \Large 6 \left(3+13a-18a^{2}+8a^{3}\right) \)
C) \( \Large 6 \left(3+13a+18a^{2}-8a^{3}\right) \)
D) \( \Large 6 \left(3-13a-18a^{2}-8a^{3}\right) \)

Correct Answer:

A) \( \Large 6 \left(3-13a+18a^{2}-8a^{3}\right) \)

Description for Correct answer:

\( \Large x^{3}+y^{3}+z^{3} \)

= \( \Large \left(2a-1\right)^{3}+ \left(2a-2\right)^{3}+ \left(3-4a\right)^{3} \)

= \( \Large 8a^{3}-1-6a \left(2a-1\right)+8a^{3}-8-12a \left(2a-2\right) \) \( \Large +27-64a^{3}-36a \left(3-4a\right) \)

=\( \Large 18-78a+108a^{2}-48a^{3} \)

= \( \Large 6 \left(3-13a+18a^{2}-8a^{3}\right) \)

Part of solved Rational expression questions and answers : >> Elementary Mathematics >> Rational expression

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Similar Questions

1). Value of \( \Large \frac{ \left(a^{2}-b^{2}\right)^{3}+ \left(b^{2}-c^{2}\right)^{3}+ \left(c^{2}-a^{2}\right)^{3} }{ \left(a-b\right)^{3}+ \left(b-c\right)^{3}+ \left(c-a\right)^{3} } \)

A). \( \Large \left(a+b\right)^{3}+ \left(b+c\right)^{3}+ \left(c+a\right)^{3} \)

B). \( \Large \left(a+b\right)+ \left(b+c\right)+ \left(c+a\right) \)

C). \( \Large \left(a+b\right)^{3}+ \left(b+c\right)^{3}+ \left(c+a\right)^{3} \)

D). \( \Large \left(a+b\right)+ \left(b+c\right)+ \left(c+a\right) \)

2). If x + y = a and xy = b, then value of \( \Large \frac{1}{x^{3}}+\frac{1}{y^{3}} \) is

A). \( \Large a^{3}-3ab \)

B). \( \Large \frac{a^{3}+3ab}{b^{3}} \)

C). \( \Large \frac{a^{3}-3ab}{b^{3}} \)

D). \( \Large a^{3}+3ab \)

3). The value of \( \Large X^{a-b} \times X^{b-c} \times X^{c-a} \) is equal to

A). 1

B). 15

C). 13

D). 2

4). Solution of \( \Large 4^{2x}=\frac{1}{32} \) is

A). \( \Large x = -5 \)

B). \( \Large x = -\frac{5}{2} \)

C). \( \Large x = \frac{5}{2} \)

D). \( \Large x = -\frac{5}{4} \)

5). If \( \Large 3^{16} \times \left(2^{x}\right)^{2}=6^{16} \), then x is

A). 4

B). -4

C). -8

D). 8

6). If \( \Large x-y=1\ and\ x^{2}+y^{2}=41, \), then value of x+y will be

A). 9 or -9

B). 1 or 9

C). -1 or 9

D). -1 or -9

7). If \( \Large x^{3}-\frac{1}{x^{3}}=14 \), then value of \( \Large x-\frac{1}{x} \) will be

A). 2

B). 3

C). 4

D). 5

8). The value of \( \Large 2^{3^{2}} \) = ?

A). 1

B). 2

C). 8

D). 16

9). The value of \( \Large \left(2^{3/4}+2^{1/2}+2^{1/4}+1\right) \left(2^{1/4-1}\right) \) =?

A). 7

B). 5

C). 1

D). 1

10). If \( \Large 16 \times 8^{n+2} \) is expressed as powers power of 2, then the power of 2 is

A). n+8

B). 2n+ 10

C). 3n + 2

D). 3n + 10