Question

5. Using the identity for difference of two squares, evaluate the following.
(a) 18 x 22
(b) 51 x 49
(c) 101 x 99
1​

Answer 1

Answer:

Identity for all the questions,

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

$a) \: 18 \times 20$

$(20 - 2)(20 + 2)$

${20}^{2} - {2}^{2}$

$400 - 4$

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$b) \: 51 \times 49$

$(50 + 1)(50 - 1)$

${(50)}^{2} - {(1)}^{2}$

$2500 - 1$

$2499$

•°•°•°•°•°•°•°•°•°•°•°

$c) \: 101 \times 99$

$(100 + 1)(100 - 1)$

${(100)}^{2} - {(1)}^{2}$

$10000 - 1$

$9999$

•°•°•°•°•°•°•°•°•°•°•°

Step-by-step explanation:

Hope it helps you out........

Answer 2

Answer:

a... 396

a... 396b...2499

a... 396b...2499c...9999

Step-by-step explanation:

(a) 18 × 22

=(20-2)(20+2)

= (a-b)(a+b) = a^2 - b^2

={(20^2) -(2^2)}

=400-4

=396 Ans...

(b) 51 × 49

= (50+1)(50-1)

={(50^2)-(1^2)}

=2500-1

=2499

(c) 101 × 99

=(100+1)(100-1)

={(100^2)-(1^2)}

=10000-1

=9999

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