Question

expand:
$(3a - 5b - c) {}^{2}$
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Answer 1

$(3a - 5b - c) {}^{2}$

Using I'd :- ( a + b+c)²

a² + b² + c ²+ 2ab + 2bc +2ca

( 3a)² +(-5b)²+(-c)² +2(3a)(-5b) +2( -5b)(-c)+2(-c)(3a)

9a² + 25b² + c² - 30ab - 10bc - 6ac

Answer 2

ANSWER

$(3a - 5b - c)^{2}$

On comparing with

$(a+b+c)^{2}$

We get =>

a = 3a , b=-5b and c=-c

Now,

$(3a-5b-c)^{2}$

=>${3a}^2$ + ${-5b}^2$ + ${-c}^2$ +2(3a)(-5b) + 2(-5b)(-c) + 2(-c)(3a)

=>9${a}^2$ +25${b}^2$ ${c}^2$ -30ab + 10bc -6ac

Hence the expanded form of

$(3a - 5b - c)^{2}$ will be

9${a}^2$ +25${b}^2$+${c}^2$ -30ab + 10bc -6ac

Remember =>

1)$(a +b + c)^{2}$

=${a}^2$ +${b}^2$ + ${c}^2$+ 2ab + 2bc + 2ca

2)$(a+b+c)^3$

= ${a}^3$+${ b}^3$ +${c}^3$+ 3(a+b)(b+c)(a+c).

Also, try to derive a formula if possible because it makes these types of algebraic expression easier to do and it is less time-consuming.

Example=>

$a^3$ +$b^3$ +$c^3$ - 3abc

= (a + b + c){$a^2$ +$b^2$ + $c^2$ - ab - bc - ca}

These types of derivatives help in some types of maths which follows the same structure.