Use suitable identities to find the following products:
(i) (x + 4) (x + 10)   (ii) (x + 8) (x - 10)   (iii) (3x + 4) (3x - 5)
(iv) (y² + 3/2)(y² - 3/2)   (v) (3 - 2x) (3 + 2x)

Solution:

Let's use algebraic Identities to proceed with the given problem.

(x + a)(x + b) = x² + (a + b)x + ab

(a + b)(a - b) = a² - b²

(i) (x + 4) (x + 10)

Using Identity: (x + a)(x + b) = x² + (a + b)x + ab

Here a = 4, b = 10

Now, let's substitute the values of 'a' and 'b' in the given identity.

(x + 4)(x + 10) = x² + (4 + 10)x + 4 × 10

= x² + 14x + 40

(ii) (x + 8) (x - 10)

Using Identity: (x + a) (x + b) = x² + (a + b)x + ab

Here a = 8, b = -10

(x + 8) (x - 10) = x² + (8 - 10)x + (8)(-10)

= x² - 2x - 80

(iii) (3x + 4) (3x - 5)

Using Identity: (x + a) (x + b) = x² + (a + b)x + ab

Here x → 3x, a = 4, b = -5

(3x + 4) (3x - 5) = (3x)² + (4 - 5)(3x) + (4)(-5)

= 9x² - 3x - 20

(iv) (y² + 3/2) (y² - 3/2)

Using identity: (a + b)(a - b) = a² - b²

Here, a = y², b = 3/2

(y² + 3/2) (y² - 3/2)

= (y²)² - (3/2)²

= y⁴ - 9/4

(v) (3 - 2x) (3 + 2x)

Using identity: (a + b)(a - b) = a² - b²

Here a = 3, b = 2x

(3 - 2x) (3 + 2x) = (3)² - (2x)²

= 9 - 4x²

☛ Check: NCERT Solutions Class 9 Maths Chapter 2

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Video Solution:

Use suitable identities to find the following products: i) (x + 4) (x + 10)  ii) (x + 8) (x - 10)  iii) (3x + 4) (3x - 5)  iv) (y² + 3/2)(y² - 3/2) v) (3 - 2x) (3 + 2x)

NCERT Solutions Class 9 Maths Chapter 2 Exercise 2.5 Question 1:

Summary:

The product of the following (x + 4)(x + 10), (x + 8)(x - 10), (3x + 4)(3x - 5), (y² + 3/2)(y² - 3/2), and (3 - 2x)(3 + 2x) using suitable identities are x² + 14x + 40, x² - 2x - 80, 9x² - 3x - 20, y⁴ - 9/4, and 9 - 4x² respectively.

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