Question

(i) \( x^{2}-8 x+16 \) (ii) \( y^{2}+20 y+100 \) (iii) \( 36 m^{2}+60 m+25 \) (iv) \( 64 x^{2}-112 x y+49 y^{2} \) (v) \( a^{2}+6 a b+9 b^{2}-c^{2} \)

Answer 1

varsha6004, hello

(i) (x-4)²

(ii) (y+10)²

(iii) (6m+5)²

(iv) (8x-7y)²

(v) (a+3b-c)(a+3b+c)

Please let me know if this helps.

Answer 2

(i) x² − 8x − 16 = 0

⇒ x² − 4x − 4x + 16 = 0

⇒ x(x − 4) − 4(x − 4) = 0

⇒ (x − 4) (x − 4) = 0

when x − 4 = 0 then x = 4

or x − 4 = 0 then x = 4

Hence, x = 4, 4 are required roots of given equation.

(ii) y² + 20y + 100

= y² + (2 × (10))y + (10 × 10)

= y² + (2 × 10 × y) + 10²

This is of the form of identity

a² + 2ab + b² = (a + b)²

y² + (2 × 10 × y) + 10² = (y + 10)²

y² + 20y + 100 = (y + 10)²

y² + 20y + 100 = (y + 10)(y + 10)

(iii) 36m² + 60m + 25

= 6²m² + 2 × 6m × 5 + 5²

This expression is of the form of identity

a² + 2ab + b² = (a + b)²

(6m)² + (2 × 6m × 5) + 5²

= (6m + 5)²

36m² + 60m + 25 = (6m + 5) (6m + 5)

(iv) 64x² – 112xy + 49y²

= 8²x² – (2 × 8x × 7y) + 7²y²

This expression is of the form of identity

a² – 2ab + b² = (a – b)²

(8x)² – (2 × 8x × 7y) + (7y)² = (8x – 7y)²

64x² – 112xy + 49y² = (8x – 7y)(8x – 7y)

(v) a² + 6ab + 9b² – c²

= a² + 2 × a × 3b + 3²b² – c²

= a² + (2 × a × 3b) + (3b)² – c²

This expression is of the form of identity

[a² + 2ab + b²] – c² = (a + b)² – c²

a² + (2 × a × 3b) + (3b)² – c² = (a + 3b)² – c²

Again this R.H.S is of the form of identity

a² – b² = (a + b)(a – b)

(a + 3b)² – c² = [(a + 3b) + c][(a + 3b) – c]

a² + 6ab + 9b² – c² = (a + 3b + c)(a + 3b – c)