Question

5. Find the squares of the following numbers using either (x + y) = x2 + 2xy + y or
(x - y)² = x² - 2xy + y²
(a) 199
(b) 103
(c) 202
(d) 395
(e) 998​

Answer 1

Answer:-

(a) 199

199 can be written as 200 - 1

So,

⟹ (199)² = (200 - 1)²

• (a - b)² = a² - 2ab + b²

⟹ (200)² - 2(200)(1) + (1)²

⟹ 40000 - 400 + 1

⟹ 39,601

∴ (199)² = 39601

_________________________

(b) 103

103 can be written as (100 + 3)²

⟹ (103)² = (100 + 3)²

• (a + b)² = a² + 2ab + b²

⟹ (100)² + 2(100)(3) + (3)²

⟹ 10000 + 600 + 9

⟹ 10,609

∴ (103)² = 10609.

________________________

(c) 202

202 can be written as (200 + 2)

⟹ (202)² = (200 + 2)²

⟹ (200)² + 2(200)(2) + (2)²

⟹ 40000 + 800 + 4

⟹ 40804

∴ (202)² = 40804

_________________________

(d) 395

395 can be written as (400 - 5)

⟹ (395)² = (400 - 5)²

⟹ (400)² - 2(400)(5) + (5)²

⟹ 160000 - 4000 + 25

⟹ 1,56,025

∴ (395)² = 156025

________________________

(e) 998

998 can be written as (1000 - 2)

⟹ (998)² = (1000 - 2)²

⟹ (1000)² - 2(1000)(2) + (2)²

⟹ 1000000 - 4000 + 4

⟹ 9,96,004

∴ (998)² = 996004.

Answer 2

Answer:

$\huge \tt \: required \: answer$

A = 39601

$\sf \implies \: \: write \: 199 \: as \: 200 - 1$

${199}^{2} = {200 - 1}^{2}$

$\sf {200 }^{2} - 2 (200)(1) + {1}^{2}$

$\sf \: 40000 - 400 + 1$

$\sf \: 39600 + 1$

$\sf \: 39601$

B = 10609

$\sf \implies \: write \: 103 \: as \: 100 + 3$

$\sf \: {100}^{2} + 2(100)(3) + {3}^{2}$

$\sf \: 10000 + 600 + 9$

$\sf \: 10609$

C = 40804

$\sf \implies \: write \: 202 \: as \: 200 + 2$

$\sf \: {202}^{2} = {20+2}^{2}$

$\sf \: {200}^{2} = {200}^{2} + 2(200)(2) + {2}^{2}$

$\sf \: 40000 + 800 + 4$

$\sf \: 40804$

D = 156025

$\sf \implies \: write \: 395 \: as \: 400 - 5$

$\sf \: {395}^{2} = {400 - 5}^{2}$

$\sf \: 400 - 2(395)(5) + {5}^{2}$

$\sf \: 160000 - 4000 + 25$

$\sf \: 15600 + 25$

$\sf \: 15625$

E = 996004

$\sf \implies \: \: write \: 998 \: as \: 1000 - 2$

$\sf \: {998}^{2} = {1000 - 2}^{2}$

$\sf \: {1000}^{2} - 2(998)(2) + {2}^{2}$

$\sf \: 1000000 - 4000 + 4$

$\sf \: 996000 + 4$

$\sf \: 996004$

Formula applied on these

(a-b)² = a²- 2ab + b²

(a+b)² = a² + 2ab + b²