Question

use (x+a) (x+b)= x2 +(a+b)x +ab, find
101×102​

Answer 1

$\underbrace\mathfrak\color{lime}{ †\: Question:–}$

101 × 102 Split the value

$\underbrace\mathfrak\color{lime}{ †\: Answer:–}$

$~~~~~~~~~~~~~101 × 102$

$~~~~~~~~~~~~~(100 × 1) × (100 ×2)$

By using identity ; ${\green{\overline{\green{\underline{\blue{\boxed{\orange{\mathtt{(x+a) (x+b)= x² +(a+b)x +ab}}}}}}}}}$

=> x = 100

=> a = 1

=> b = 2

$(100 + 1)(100 + 2)=(100)²+(1 + 2)100 +(1)(2)$

$~~~~~~~~~~~~~ = 10000 + (200 + 100) + 2$

$~~~~~~~~~~~~~= 10000 + 300 + 2$

$~~~~~~~~~~= 10302$

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More information ;

${\green{\overline{\green{\underline{\blue{\boxed{\red{\mathtt{ (a + b)² = a² + 2ab + b²}}}}}}}}}$

${\green{\overline{\green{\underline{\blue{\boxed{\green{\mathtt{ (a - b)² = a² - 2ab + b²}}}}}}}}}$

${\green{\overline{\green{\underline{\blue{\boxed{\pink{\mathtt{a² – b² = (a + b)(a – b)}}}}}}}}}$

${\green{\overline{\green{\underline{\blue{\boxed{\orange{\mathtt{(x+a) (x+b)= x² +(a+b)x +ab}}}}}}}}}$

Answer 2

Answer:

10302

Step-by-step explanation:

101 = 100 + 1

102 = 100 + 2

101 × 102

= ( 100 + 1 ) ( 100 + 2 )

= ( 100 )^2 + ( 1 + 2 )100 + ( 1 ) ( 2 )

= 10000 + 300 + 2

= 10302