The correct option is B 10098We know the identity, (x+a)(x+b)=x^2+(a+b)x + ab Given: 102×99 ⇒(100 + 2)×(100+( 1)) ⇒100^2 + (2+( 1))100+2×( 1) ⇒100^2 + (1)100+ ...

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Byju's Answer

Standard IX

Mathematics

Visualisation of (X+A)(X+B)

102 × 99=

Question

102 X 99 =

11098

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10098

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10980

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Solution

The correct option is B 10098
We know the identity,
$(x + a) (x + b) = x^{2} + (a + b) x + a b$

Given: $102 \times 99$
$\Rightarrow (100 + 2) \times (100 + (- 1))$
$\Rightarrow 100^{2} + (2 + (- 1)) 100 + 2 \times (- 1)$
$\Rightarrow 100^{2} + (1) 100 + 2 \times (- 1)$
$\Rightarrow 100^{2} + 100 - 2$
$\Rightarrow 10000 + 98$
$\Rightarrow 10098$

Thus, $102 \times 99 = 10098$

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Similar questions

99 \sum r = 1 r! (r^{2} + r + 1) =

Q. Using binomial theorem, evaluate each of the following:
i)

(102)^{3}

(ii)

(99)^{3}

Q. Given

\sum x = 99, n = 9

and

\sum (x - 10)^{2} = 79

. Find

\sum x^{2}

and

\sum (x - ¯ x)^{2}

Evaluate the following using suitable identities:

(i) (99)³ (ii) (102)³ (iii) (998)³

Evaluate the following using suitable identities:
(i) $(99)^{3}$
(ii) $(102)^{3}$
(iii) $(998)^{3}$

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102 X 99 =

The correct option is B 10098We know the identity, (x+a)(x+b)=x2+(a+b)x+ab Given: 102×99 ⇒(100+2)×(100+(−1)) ⇒1002+(2+(−1))100+2×(−1) ⇒1002+(1)100+2×(−1) ⇒1002+100−2 ⇒10000+98 ⇒10098 ​​​​​​​ Thus, 102×99=10098