Question

1. Use a suitable identity to get each of the following products.
0 (x+3)(x + 3) (i) (2y + 5) (2y + 5) (m) (2a-7) (2a - 7)​

Answer 1

Solution:-

i) (x + 3)(x + 3)

⇒ (x + 3)²

[Identity used: (a + b)² = a² + b² + 2ab ]

⇒ x² + 3² + 2 * x * 3

⇒ x² + 9 + 6x

⇒ x² + 6x + 9 [Answer]

$\rule{200}{1}$

ii) (2y + 5)(2y + 5)

⇒ (2y + 5)²

[Identity used: (a + b)² = a² + b² + 2ab ]

⇒ (2y)² + 5² + 2 × 2y × 5

⇒ 4y² + 25 + 20y

⇒ 4y² + 20y + 25 [Answer]

$\rule{200}{1}$

iii) (2a - 7)(2a - 7)

⇒ (2a - 7)²

[Identity used: (a - b)² = a² + b² - 2ab ]

⇒ (2a)² + 7² - 2 × 2a × 7

⇒ 4a² + 49 - 28a

⇒ 4a² - 28a + 49 [Answer]

$\rule{200}{4}$

Similar more identities:-

• a² - b² = (a + b)(a - b)
• (x + a)(x + b) = x² + (a + b)x + ab
• (a + b)² = (a - b)² + 4ab
• (a - b)² = (a + b)² - 4ab
• a² + b² = (a + b)² - 2ab
• a² + b² = (a - b)² + 2ab

Answer 2

Answer:

(i)x(x+3)+3(x+3)

=x^2+3x+3x+9

=x^2+6x+9 ans

(ii)(2y+5)(2y+5)

=2y(2y+5)+5(2y+5)

=4y^2+10y+10y+25

=4y^2+20y+25 ans

(iii)(2a-7)(2a-7)

=2a(2a-7)-7(2a-7)

=4a^2-14a-14a+49

=4a^a-28a+49 ans

Step-by-step explanation:

I hope its help you