In the expansion of 2 a -3 a -22- find the coefficient of a 2 and aA- i -11 ii -20B- i 11 ii 20C- i 8 ii 12D- i 9 ii 3

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Standard XI

Mathematics

Binomial Expression

In the expans...

Question

In the expansion of $(2 a + 3) (a + 2)^{2}$ ; find the coefficient of $a^{2}$ and $a$

(i) -11 (ii) -20

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(i) 11 (ii) 20

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(i) 8 (ii) 12

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(i) 9 (ii) 3

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Solution

The correct option is B
(i) 11 (ii) 20

$(2 a + 3) (a + 2)^{2} = (2 a + 3) (a^{2} + (2) (2) (a) + 2^{2}$ )
= $2 a^{3} + 8 a^{2} + 8 a + 3 a^{2} + 12 a + 12$
= $2 a^{3} + 11 a^{2} + 20 a + 12$
Hence the coefficient of $a^{2}$ = 11 and coefficient of $a$ = 20.

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In the expansion of (2a+3)(a+2)2 ; find the coefficient of a2 and a

The correct option is B (i) 11 (ii) 20 (2a+3)(a+2)2=(2a+3)(a2+(2)(2)(a)+22) = 2a3+8a2+8a+3a2+12a+12 = 2a3+11a2+20a+12 Hence the coefficient of a2 = 11 and coefficient of a = 20.

In the expansion of $(2 a + 3) (a + 2)^{2}$ ; find the coefficient of $a^{2}$ and $a$

The correct option is B
(i) 11 (ii) 20

$(2 a + 3) (a + 2)^{2} = (2 a + 3) (a^{2} + (2) (2) (a) + 2^{2}$ )
= $2 a^{3} + 8 a^{2} + 8 a + 3 a^{2} + 12 a + 12$
= $2 a^{3} + 11 a^{2} + 20 a + 12$
Hence the coefficient of $a^{2}$ = 11 and coefficient of $a$ = 20.