Question

plz help i need help

Answer 1

hope this helps you....

Answer 2

QUESTION:

Find the square of the following numbers without actual multiplication.

• a) 19

• b) 23

• c) 45

• d) 52

ANSWER:

• a) 19² = 361

• b) 23² = 529

• c) 45² = 2025

• d) 52² = 2704

GIVEN:

• a) 19

• b) 23

• c) 45

• d) 52

TO FIND:

• Squares of the numbers without actual multiplication.

EXPLANATION:

$\rule{200}{2}$

• a) 19² = (20 - 1)²

$\boxed{ \bold{ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} }}$

• (20 - 1)² = 20² - 2(20)(1) + 1²

• (20 - 1)² = 400 - 2(20) + 1

• (20 - 1)² = 360 + 1

• (20 - 1)² = 19² = 361

$\rule{200}{2}$

• b) 23² = (20 + 3)²

$\boxed{ \bold{ {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} }}$

• (20 + 3)² = 20² + 2(3)(20) + 3²

• (20 + 3)² = 400 + 120 + 9

• (20 + 3)² = 520 + 9

• 23² = (20 + 3)² = 529

$\rule{200}{2}$

• c) 45² = (40 + 5)²

$\boxed{ \bold{ {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} }}$

• (40 + 5)² = 40² + 2(5)(40) + 5²

• (40 + 5)² = 1600 + 400 + 25

• (40 + 5)² = 2000 + 25

• 45² = (40 + 5)² = 2025

$\rule{200}{2}$

• d) 52² = (50 + 2)²

$\boxed{ \bold{ {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} }}$

• (50 + 2)² = 50² + 2(2)(50) + 2²

• (50 + 2)² = 2500 + 200 + 4

• (50 + 2)² = 2700 + 4

• 52² = (50 + 2)² = 2704

$\rule{200}{2}$

★a)19² = 361

★b) 23² = 529

★c) 45² = 2025

★d) 52² = 2704

$\rule{200}{2}$