How to factorise the following quadratics? yr 9

a) 9b² + 48b + 64
b) (ac)² - d²
c) a² + ab - 182 b²
d) b² - 2abc + a²c²

pls i am so clueless. so pls show all working.
thanks so much

a) 9b² + 48b + 64
= 9b² + 24b + 24b + 64
= 3b(3b + 8) + 8(3b + 8)
= 3b(3b + 8) + 8(3b + 8)
= (3b + 8)(3b + 8)

b) (ac)² - d²
= (ac + d)(ac – d)

c) a² + ab - 182 b²
= a² + 13ab – 14ab - 182 b²
= a(a + 13b) – 14b(a + 13b)
= (a – 14b)(a + 13b)

d) b² - 2abc + a²c²
= b² – abc – abc + a²c²
= b(b – ac) – ac(b – ac)
= (b – ac) (b – ac)
-------

a) USE FORMULA ( a^2 + 2ab +b^2) = ( a+b)^2

9b^2 + 48b + 64 = (3b)^2 + 2 (3b) (8) + (8)^2 = ( 3b +8)^2 ANSWER


b) (ac)^2 - d^2

USE FORMULA a^2 - b^2 = ( a+b) ( a - b)

( ac + d) (ac- d) ANSWER

c) Find factors of - 182 which add up to +1 ( coeff of ab)

a^2 + 14ab -13ab -182b^2

a ( a +14b) -13b (a + 14b)

( a-13b) ( a+14b) ANSWER

d) b^2 - 2abc + a^2c^2

USE FORMULA a^2 - 2ab + b^2 = ( a - b) ^2

b^2 - 2abc + a^2c^2 = ( b - ac ) ^2 ANSWER

a) (3b+8)^2 -> square of first, plus 2 times the product of the first and second, plus square of second.
b) (a c-d) (a c+d) -> Expand Squares
c) (a-13 b) (a+14 b)
d) (b-a c)^2