# Use a suitable identity to get each of the following products

(i) (x + 3)(x + 3) (ii) (2y + 5)(2y + 5)

(iii) (2a - 7)(2a - 7) (iv) (3a - (1/2))(3a - (1/2))

(v) (1.1 m - 0.4)(1.1 m + 0.4) (vi)(a^{2} + b^{2})(-a^{2} + b^{2})

(vii) (6x - 7)(6x + 7) (viii) (-a + c)(-a + c)

(ix) (x/2 + 3y/4)(x/2 + 3y/4) (x) (7a - 9b)(7a - 9b)

**Solution:**

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

= (x + 3)^{2}

= (x)^{2 }+ 2(x)(3) + (3)^{2} [Using the algebraic identity (a + b)^{2} = a^{2} + 2ab + b^{2}]

= x^{2} + 6x + 9

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

= (2y + 5)^{2}

= (2y)^{2} + 2(2y)(5) + (5)^{2} [Since, (a + b)^{2} = a^{2} + 2ab + b^{2}]

= 4y^{2} + 20y + 25

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

= (2a - 7)^{2}

= (2a)^{2 }- 2(2a)(7) + (7)^{2 } [Since, (a - b)^{2} = a^{2} - 2ab + b^{2}]

= 4a^{2} - 28a + 49

(iv) (3a - (1/2))(3a - (1/2))

= (3a - (1/2))^{2}

= (3a)^{2} - 2(3a)(1/2) + (1/2)^{2 } [Since, (a - b)^{2} = a^{2} - 2ab + b^{2}]

= 9a^{2} - 3a + 1/4

(v) (1.1m - 0.4)(1.1m + 0.4)

= (1.1m)^{2} - (0.4)^{2} [Since, (a + b)(a - b) = a^{2} - b^{2}]

= 1.21m^{2} - 0.16

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

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

= (b^{2})^{2} - (a^{2})^{2} [Since, (a + b)(a - b) = a^{2} - b^{2}]

= b^{4} - a^{4}

(vii) (6x - 7)(6x + 7)

= (6x)^{2} - (7)^{2 } [Since, (a + b)(a - b) = a^{2} - b^{2}]

= 36x^{2} - 49

(viii) (-a + c)(-a + c)

= (-a + c)^{2}

= (-a)^{2} + 2(-a)(c) + (c)^{2 } [Since, (a + b)^{2} = a^{2} + 2ab + b^{2}]

= a^{2} - 2ac + c^{2}

(ix) (x/2 + 3y/4)(x/2 + 3y/4)

= (x/2 + 3y/4)^{2}

= (x/2)^{2} + 2(x/2)(3y/4) + (3y/4)^{2} [Since, (a + b)^{2} = a^{2} + 2ab + b^{2}]

= x^{2}/4 + 3xy/4 + 9y^{2}/16

(x) (7a - 9b)(7a - 9b)

= (7a - 9b)^{2}

= (7a)^{2} - 2(7a)(9b) + (9b)^{2} [Since, (a - b)^{2} = a^{2} - 2ab + b^{2}]

= 49a^{2} -126ab + 81b^{2}

**☛ Check: **NCERT Solutions for Class 8 Maths Chapter 9

**Video Solution:**

## Use a suitable identity to get each of the following products (i) (x + 3)(x + 3) (ii) (2y + 5)(2y + 5) (iii) (2a - 7)(2a - 7) (iv) (3a - (1/2))(3a - (1/2)) (v) (1.1 m - 0.4)(1.1 m + 0.4) (vi)(a^{2} + b^{2})(-a^{2} + b^{2}) (vii) (6x - 7)(6x + 7) (viii) (-a + c)(-a + c) (ix) (x/2 + 3y/4)(x/2 + 3y/4) (x) (7a - 9b)(7a - 9b)

NCERT Solutions Class 8 Maths Chapter 9 Exercise 9.5 Question 1

**Summary:**

The product of the given expressions (i) (x + 3)(x + 3) (ii) (2y + 5)(2y + 5) (iii) (2a - 7)(2a - 7) (iv) (3a - (1/2))(3a - (1/2)) (v) (1.1 m - 0.4)(1.1 m + 0.4) (vi)(a^{2} + b^{2})(-a^{2} + b^{2}) (vii) (6x - 7)(6x + 7) (viii) (-a + c)(-a + c) (ix) (x/2 + 3y/4)(x/2 + 3y/4) (x) (7a - 9b)(7a - 9b) are i) x^{2} + 6x + 9 ii) 4y^{2} + 20 y + 25 iii) 4a^{2} - 28a + 49 iv) 9a^{2} - 3a + 1/4 v) 1.21m^{2} - 0.16 vi) b^{4} - a^{4} vii) 36x^{2} - 49 viii) a^{2} - 2ac + c^{2} ix) x^{2}/4 + 3xy/4 + 9y^{2}/16 x) 49a^{2} -126ab + 81b^{2}

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