# Use suitable identities to find the following products:

(i) (x + 4) (x + 10) (ii) (x + 8) (x - 10) (iii) (3x + 4) (3x - 5)

(iv) (y^{2} + 3/2)(y^{2} - 3/2) (v) (3 - 2x) (3 + 2x)

**Solution:**

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

(x + a)(x + b) = x^{2} + (a + b)x + ab

(a + b)(a - b) = a^{2} - b^{2}

**(i)** (x + 4) (x + 10)

Using Identity: (x + a)(x + b) = x^{2} + (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) = x^{2} + (4 + 10)x + 4 × 10

= x^{2} + 14x + 40

**(ii)** (x + 8) (x - 10)

Using Identity: (x + a) (x + b) = x^{2} + (a + b)x + ab

Here a = 8, b = -10

(x + 8) (x - 10) = x^{2} + (8 - 10)x + (8)(-10)

= x^{2} - 2x - 80

**(iii)** (3x + 4) (3x - 5)

Using Identity: (x + a) (x + b) = x^{2} + (a + b)x + ab

Here x → 3x, a = 4, b = -5

(3x + 4) (3x - 5) = (3x)^{2} + (4 - 5)(3x) + (4)(-5)

= 9x^{2} - 3x - 20

**(iv)** (y^{2} + 3/2) (y^{2} - 3/2)

Using identity: (a + b)(a - b) = a^{2} - b^{2}

Here, a = y^{2}, b = 3/2

(y^{2} + 3/2) (y^{2} - 3/2)

= (y^{2})^{2} - (3/2)^{2}

= y^{4} - 9/4

**(v)** (3 - 2x) (3 + 2x)

Using identity: (a + b)(a - b) = a^{2} - b^{2}

Here a = 3, b = 2x

(3 - 2x) (3 + 2x) = (3)^{2} - (2x)^{2}

= 9 - 4x^{2}

**☛ Check: **NCERT Solutions Class 9 Maths Chapter 2

**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), (y^{2 }+ 3/2)(y^{2 }- 3/2), and (3 - 2x)(3 + 2x) using suitable identities are x^{2 }+ 14x + 40, x^{2 }- 2x - 80, 9x^{2 }- 3x - 20, y^{4 }- 9/4, and 9 - 4x^{2 }respectively.

**☛ Related Questions:**

- Evaluate the following products without multiplying directly:(i) 103 × 107(ii) 95 × 96(iii) 104 × 96
- Factorise the following using appropriate identities:(i) 9x2 + 6xy + y2(ii) 4y2 - 4y + 1(iii) x2 - y2/100
- Expand each of the following, using suitable identities:i) (x + 2y + 4z)²ii) (2x - y + z)²iii) (-2x + 3y + 2z)²iv) (3a - 7b - c)²v) (-2x + 5y - 3z)²vi) [(1/4)a - (1/2)b + 1]²

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