Question

Use the given identity and solve. (1) (6x – 3y)2 :- Identity II (2) 105 X 102 :- Identity IV​

Answer 1

Solution

$\colorbox{silver}{ \boxed{ \begin{array}{c} \sf {(6x - 3y)}^{2} \\ \sf \: using \: identity \: {(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab \: \\ \sf \: \pmb{ \bf{(6x - 3y)}^{2} = 36 {x}^{2} + 9 {y}^{2} - 36xy } \\ \\ \hline105 \times 102 \\ \sf \: using \: identity \: (x + a)(x + b) = {x}^{2} + x(a + b) + ab \\ (100 + 5)(100 + 2) = {100}^{2} + 100(5 + 2) + 10 \\ = 10000 + 700 + 10 = \bf10710 \end{array}}}$

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Answer 2

Answer:

Solution

\begin{gathered} \colorbox{silver}{ \boxed{ \begin{array}{c} \sf {(6x - 3y)}^{2} \\ \sf \: using \: identity \: {(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab \: \\ \sf \: \pmb{ \bf{(6x - 3y)}^{2} = 36 {x}^{2} + 9 {y}^{2} - 36xy } \\ \\ \hline105 \times 102 \\ \sf \: using \: identity \: (x + a)(x + b) = {x}^{2} + x(a + b) + ab \\ (100 + 5)(100 + 2) = {100}^{2} + 100(5 + 2) + 10 \\ = 10000 + 700 + 10 = \bf10710 \end{array}}}\end{gathered}

(6x−3y)

2

usingidentity(a−b)

2

=a

2

+b

2

−2ab

(6x−3y)

2

=36x

2

+9y

2

−36xy

(6x−3y)

2

=36x

2

+9y

2

−36xy

105×102

usingidentity(x+a)(x+b)=x

2

+x(a+b)+ab

(100+5)(100+2)=100

2

+100(5+2)+10

=10000+700+10=10710

Hope this helps you ♡