# Factorize the following expressions.

(i) a^{2} + 8a +16 (ii) p^{2} - 10 p + 25 (iii) 25m^{2} + 30m + 9

(iv) 49 y^{2} + 84 yz + 36z^{2 }(v) 4x^{2} - 8x + 4

(vi) 121b^{2} - 88bc +16c^{2 }(vii) (l +m)^{2} - 4lm (Hint: Expand (l + m)^{2} first)

(viii) a^{4}+ 2a^{2}b^{2} + b^{4}

**Solution:**

(i) a^{2} + 8a +16

= (a)^{2} + 2 × a × 4 + (4)^{2}

= (a + 4)^{2 }[Using identity (x + y)^{2} = x^{2} + 2xy + y^{2}, considering x = a and y = 4 ]

(ii) p^{2} - 10 p + 25

= (p)^{2} - 2 × p × 5 + (5)^{2}

= (p - 5)^{2 }[Using identity (a - b)^{2} = a^{2} - 2ab + b^{2}, considering a = p and b = 5 ]

(iii) 25m^{2} + 30m + 9

= (5m)^{2} + 2 × 5m × 3 + (3)^{2}

= (5m + 3)^{2 }[Using identity (a + b)^{2} = a^{2} + 2ab + b^{2}, considering a = 5m and b = 3 ]

(iv) 49y^{2} + 84yz + 36z^{2}

= (7y)^{2} + 2 × (7y) × (6z) + (6z)^{2}

= (7y + 6z)^{2 }[Using identity (a + b)^{2} = a^{2} + 2ab + b^{2}, considering a = 7y and b = 6z]

(v) 4x^{2} - 8x+ 4

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

= (2x - 2)^{2 }[Using identity (a - b)^{2} = a^{2} - 2ab + b^{2}, considering a = 2x and b = 2]

= [(2)(x -1)]^{2} = 4(x -1)^{2}

(vi) 121b^{2} - 88bc+16c^{2}

= (11b)^{2} - 2(11b)(4c) + (4c)^{2}

= (11b - 4c)^{2 }[Using identity (a - b)^{2} = a^{2} - 2ab + b^{2}, considering a = 11b and b = 4c]

(vii) (l + m)^{2} - 4lm

= l^{2} + 2lm+ m^{2} - 4lm [Using identity (a + b)^{2} = a^{2} + 2ab + b^{2}]

= l^{2} - 2lm + m^{2 }

= (l - m)^{2} [Using identity (a - b)^{2} = a^{2} - 2ab + b^{2}, considering a = l and b = m]

(viii) a^{4} + 2a^{2}b^{2} + b^{4}

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

= (a^{2} + b^{2})^{2 } [Using identity (x + y)^{2} = x^{2} + 2xy + y^{2}, considering x = a^{2} and y = b^{2}]

**☛ Check: **NCERT Solutions for Class 8 Maths Chapter 14

**Video Solution:**

## Factorize the following expressions. (i) a² + 8a +16 (ii) p² -10 p + 25 (iii) 25m² + 30m + 9 (iv) 49 y² + 84 yz + 36z²^{ }(v) 4x² - 8x + 4 (vi) 121b² - 88bc +16c²^{ }(vii) (l +m)² - 4lm (Hint: Expand (l + m)² first) (viii) a⁴+ 2a²b² + b⁴

Class 8 Maths NCERT Solutions Chapter 14 Exercise 14.2 Question 1

**Summary:**

The following expressions (i) a^{2} + 8a +16 (ii) p^{2} -10 p + 25 (iii) 25m^{2} + 30m + 9 (iv) 49 y^{2} + 84 yz + 36z^{2 }(v) 4x^{2} - 8x + 4 (vi) 121b^{2} - 88bc +16c^{2 }(vii) (l +m)^{2} - 4lm (viii) a^{4}+ 2a^{2}b^{2} + b^{4} are factorised as (i) (a + 4)^{2 } (ii) (p- 5)^{2 } (iii) (5m + 3)^{2 } (iv) (7y + 6z)^{2 } (v) 4(x -1)^{2} (vi) (11b - 4c)^{2 }(vii) (l - m)^{2} (viii) (a^{2} + b^{2})^{2}

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