Question

3. Simplify each of the following:
(i) 175 x 175 + 2 x 175 x 25 + 25 x 25 (ii) 322 x 322 – 2 x 322 x 22 + 22 x 22
7.83 x 7.83 - 1.17 x 1.17
(iii) 0.76 x 0.76 + 2 x 0.76 x 0.24 +0.24 x 0.24

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Answer 1

in first we will use the formula of a plus b whole square is equal to a square + 2 a b + b square so it is given a square + 2 a b + b square so we will make the answer as a + b whole square then our solution will become easier.

(a+b)^2

(175+25)^2

(200)^2

40000

so we will do same as we have done in the first question ok we will use the formula of a plus b whole square is equal to a square minus 2 a b + b square

(322-22)^2

(300)^2

90000

it is same we have done in first question a + b whole square is equal to a square + b square + 2 Ab

(0.76+0.24)^2

(1)^2

1

Answer 2

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

1). 175 × 175 + 2 × 175 × 25 + 25 × 25

= (175)² + 2(175)(25) + (25)²

= (175 + 25)²

Now,

Assume :-

x = 175 and also y = 25

So,

Using Identity :-

(x + y)² = x² + y² + 2xy

So,

= (200)²

= 40000

$\rule{300}{1.5}$

2). 322 × 322 - 2 × 322 × 22 + 22 × 22

= (322)² - 2 × 322 × 22 + (22)²

= (322 - 22)²

Assume :-

x = 322 and also y = 22

So,

Using Identity :-

(x - y)² = x² + y² - 2xy

So,

= (300)²

= 90000

$\rule{300}{1.5}$

3). 0.76 × 0.76 + 2 × 0.76 × 0.24 + 0.24 × 0.24

= (0.76)² + 2 × 0.76 × 0.24 + (0.24)²

= (0.76 + 0.24)²

Assume :-

x = 0.76 and also y = 0.24

So,

Using Identity :-

(x + y)² = x² + y² + 2xy

So,

= (1.00)²

= 1