# Find the following squares by using the identities

(i)(b - 7)^{2 }(ii) (xy + 3z)^{2 }(iii) (6x^{2} - 5y)^{2}

(iv) (2m/3 + 3n/2)^{2 }(v) (0.4p - 0.5q)^{2 }(vi) (2xy + 5y)^{2}

**Solution:**

We will be using the following algebraic identities

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

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

(i) (b - 7)^{2}

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

= b^{2} - 14b + 49

(ii) (xy + 3z)^{2}

= (xy)^{2 }+ 2(xy)(3z) + (3z)^{2} [Since, (a + b)^{2} = a^{2} + 2ab + b^{2}]

= x^{2}y^{2} + 6xyz + 9z^{2}

(iii) (6x^{2} - 5y)^{2}

= (6x^{2})^{2} - 2(6x^{2})(5y) + (5y)^{2} [Since, (a - b)^{2} = a^{2} - 2ab + b^{2}]

= 36x^{4} - 60x^{2}y + 25y^{2}

(iv) (2m/3 + 3n/2)^{2}

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

= 4m^{2}/9 + 2mn + 9n^{2}/4

(v) (0.4p - 0.5q)^{2}

= (0.4p)^{2} - 2(0.4p)(0.5q) + (0.5q)^{2} [Since, (a - b)^{2} = a^{2} - 2ab + b^{2}]

= 0.16p^{2} - 0.4pq + 0.25q^{2}

(vi) (2xy + 5y)^{2}

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

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

The squares of the given expressions are i) b^{2} - 14b + 49 ii) x^{2}y^{2} + 6xyz + 9z^{2} iii) 36x^{4} - 60x^{2}y + 25y^{2} iv) 4m^{2}/9 + 2mn + 9n^{2}/4 v) 0.16p^{2} - 0.4pq + 0.25q^{2} vi) 4x^{2}y^{2} + 20xy^{2} + 25y^{2}

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

**Video Solution:**

## Find the following squares by using the identities (i)(b - 7)^{2 }(ii) (xy + 3z)^{2 }(iii) (6x^{2} - 5 y)^{2 }(iv) (2m/3 + 3n/2)^{2 }(v) (0.4 p - 0.5q)^{2 }(vi) (2xy + 5 y)^{2}

NCERT Solutions Class 8 Maths Chapter 9 Exercise 9.5 Question 3

**Summary:**

The squares of the given expressions using suitable identities (i)(b - 7)^{2 }(ii) (xy + 3z)^{2 }(iii) (6x^{2} - 5 y)^{2 }(iv) (2m/3 + 3n/2)^{2 }(v) (0.4 p - 0.5q)^{2 }(vi) (2xy + 5 y)^{2} are i) b^{2} - 14b + 49 ii) x^{2}y^{2} + 6xyz + 9z^{2} iii) 36x^{4} - 60x^{2}y + 25y^{2} iv) 4m^{2}/9 + 2mn + 9n^{2}/4 v) 0.16p^{2} - 0.4pq + 0.25q^{2} vi) 4x^{2}y^{2} + 20xy^{2} + 25y^{2}

**☛ Related Questions:**

- Show that (i)(3x + 7)2 - 84x = (3x - 7)2 (ii) (9p - 5q)2 + 180pq = (9p + 5q)2 (iii) (4m/3 - 3n/4)2 + 2mn = 16m2/9 + 9n2/16 (iv) (4pq + 3q)2 - (4pq - 3q)2 = 48pq2 (v) (a - b)(a + b) + (b - c)(b + c) + (c - a)(c + a) = 0
- Using identities, evaluate. i) 712 ii) 992 iii) 1022 iv) 9982 v) (5.2)2 vi) 297 × 303 vii) 78 × 82 viii) 8.92 ix) 1.05 × 9.5
- Using a2 - b2 = (a + b)(a - b), find (i) 512 – 492 (ii) (1.02)2 - (0.98)2 (iii) 1532 -1472 (iv) 12.12 - 7.92
- Using (x + a)(x + b) = x2 + (a + b)x + ab (i) 103 × 104 (ii) 5.1 × 5.2 (iii) 103 × 98 (iv) 9.7 × 9.8

visual curriculum