Calculate 103 - 107 using algebraic identities-10121110211002112011

The correct option is B 11021 We know that nbsp;( x + a ) ( x + b ) = x^2 nbsp;+ ( a + b )x + ab To split 103 × 107, we need a square that is easy to calcu ...

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Standard IX

Mathematics

Identity (x+a)(x+b)

Calculate 103...

Question

Calculate $103 \times 107$ using algebraic identities.

10121

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11021

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Solution

The correct option is B 11021

We know that $(x + a) (x + b) = x^{2} + (a + b) x + a b$

To split $103 \times 107$ , we need a square that is easy to calculate.

Hence, $x = 100, a = 3, b = 7$

$∴ 103 \times 107 = (100 + 3) (100 + 7)$
$= 100^{2} + (3 + 7) (100) + (3) (7)$
$= 10000 + 1000 + 21 = 11021$

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Calculate 103×107 using algebraic identities.

The correct option is B 11021 We know that (x+a)(x+b)=x2+(a+b)x+ab To split 103×107, we need a square that is easy to calculate. Hence, x=100,a=3,b=7 ∴103×107=(100+3)(100+7) =1002+(3+7)(100)+(3)(7) =10000+1000+21=11021

Calculate $103 \times 107$ using algebraic identities.