Evaluate the product 104 - 96 without multiplying directly

Multiplication:Given expression can be written as104 × 96 = (100 + 4) × (100 – 4)Using identity(a + b)(a – b)= a^2 – b^2Herea = 100, b = 4⇒ (100 + 4) × (100 ...

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Standard VIII

Mathematics

Cube Numbers

Evaluate the ...

Question

Evaluate the product $104 \times 96$ without multiplying directly

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Solution

Multiplication:
Given expression can be written as
$104 \times 96 = (100 + 4) \times (100 - 4)$
Using identity
$(a + b) (a - b) = a^{2} - b^{2}$
Here
$a = 100, b = 4$
$\Rightarrow (100 + 4) \times (100 - 4) = {(100)}^{2} - {(4)}^{2} = 10000 - 16 = 9984$
Hence the product is $9984$

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Evaluate the product 104×96 without multiplying directly

Multiplication:Given expression can be written as104×96=(100+4)×(100–4)Using identity(a+b)(a–b)=a2–b2Herea=100,b=4⇒(100+4)×(100–4)=(100)2–(4)2=10000–16=9984Hence the product is 9984

Evaluate the product $104 \times 96$ without multiplying directly

Multiplication:
Given expression can be written as
$104 \times 96 = (100 + 4) \times (100 - 4)$
Using identity
$(a + b) (a - b) = a^{2} - b^{2}$
Here
$a = 100, b = 4$
$\Rightarrow (100 + 4) \times (100 - 4) = {(100)}^{2} - {(4)}^{2} = 10000 - 16 = 9984$
Hence the product is $9984$