Question

Evaluate by using (a² - b²) = (a - b) (a + b)(1) 97 X 103
(2) 57 X 63
(3) 34 x 26

Answer 1

Answer:

(1) a=100 b=3

(2) a=60 b=3

(3) a=30 b=4

Answer 2

Answer:

The result is:

1. 9991

2. 3591

3. 884

Step-by-step explanation:

Given expression is:

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

__Part 1.)__

$97\times 103$

We can write as:

$97=100-3\\103=100+3$

Hence plugging the value of 100 and 3 with respect to a and b we get:

$(100)^2-(3)^2\\=1000-9\\=9991$

And also:

$103\times 97\\=9991$

__Part 2.)__

$57\times 63$

We may write as:

$57=60-3\\63=60+3$

Plugging the value of 60 and 3 in place of a and b.

Hence:

$(60)^2-(3)^2\\=3600-9\\3591$

And

$57\times 63\\=3591$

__Part 3.)__

$34\times 26$

We may write as:

$34=30+4\\26=30-4$

Plugging the value of 30 and 4 in place a and b we get:

$(30)^2-(4)^2\\=900-16\\=884$

And

$34\times 26\\=884$