Question

using (x + a) (x+b) =x² + (a+b) x + ab, find . (i) 5.1 × 5.2 , (ii) 103× 98​

Answer 1

$\large\underline{\sf{Solution-(i)}}$

$\rm :\longmapsto\:5.1 \times 5.2$

can be rewritten as

$\rm \:  =  \: (5 + 0.1)(5 + 0.2)$

So, using identity,

$\rm :\longmapsto\:\boxed{\tt{ (x + a)(x + b) = {x}^{2} + (a + b)x + ab}}$

So, here,

$\rm :\longmapsto\:x = 5$

$\rm :\longmapsto\:a = 0.1$

$\rm :\longmapsto\:b = 0.2$

On substituting the values, we get

$\rm \:  =  \: {5}^{2} + (0.1 + 0.2)5 + (0.1)(0.2)$

$\rm \:  =  \: 25+ (0.3)5 + 0.02$

$\rm \:  =  \: 25.02+ 1.5$

$\rm \:  =  \: 26.52$

$\red{\large\underline{\sf{Solution-ii}}}$

$\red{\rm :\longmapsto\:103 \times 98}$

$\red{\rm \:  =  \: (100 + 3)(100 - 2)}$

So, using identity,

$\red{\rm :\longmapsto\:\boxed{\tt{ (x + a)(x + b) = {x}^{2} + (a + b)x + ab}}}$

So, here,

$\red{\rm :\longmapsto\:x = 100}$

$\red{\rm :\longmapsto\:a = 3}$

$\red{\rm :\longmapsto\:b = - 2}$

So, on substituting the values, we get

$\red{\rm \:  =  \: {100}^{2} + (3 - 2)100 - 3 \times 2}$

$\red{\rm \:  =  \: 10000 + 100 - 6}$

$\red{\rm \:  =  \: 10000 + 94}$

$\red{\rm \:  =  \: 10094}$

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More to Know :-

$\boxed{\tt{ {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2}}}$

$\boxed{\tt{ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2}}}$

$\boxed{\tt{ {(x + y)}^{3} = {x}^{3} + 3xy(x + y) + {y}^{3}}}$

$\boxed{\tt{ {(x - y)}^{3} = {x}^{3} - 3xy(x - y) - {y}^{3}}}$

$\boxed{\tt{ {x}^{2} - {y}^{2} = (x + y)(x - y)}}$