Question

Expand the following using suitable identities:
(i) (3a − 7b − c )sq (ii) (2a − 3b )cube

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Answer 1

Answer:

1. $\sf \: identity \: is \: (a+b+c) {}^{2} = a^2+b^2+c^2+\\2ab+2bc+2ca$

$\sf \: now \: expand \: it \: by \: putting \\ \sf \: a = 3a, b = (-7b), c= (-c)$

$\sf \: substitute \: the \: values \: and \: you \: will \\ \sf \: get \: the \: answer$

$\sf \: = 9a^2+49b^2+c^2-42ab+14bc-6ca$

2.We need to expand (2a-3b)³.

2.We need to expand (2a-3b)³.We know suitable identity for it is

$\sf(x - y) {}^{3} = {x}^{3} - 3 {x}^{2} y + 3x {y}^{2} + {y}^{3}$

Here x= 2a and y= 3b

Therefore the value of (2a-3b)³ is

$\sf = ( {2a})^{3} - 3( {2a})^{2} (3b) + 3(2a)(3b) {}^{2} - (3b) {}^{3}$

$\sf = 8 {a}^{3} - 36 {a}^{2} b + 54 {ab}^{2} - 27 {b}^{3}$