Maths Factorize (7Q, 20 Marks)

Factorize the following
1. 75(c - 3d) ^2 - 27(2c-5d)^2
3[5^2(c - 3d) ^2 – 3^2(2c-5d)^2]
3[(5(c - 3d)) ^2 – (3(2c-5d))^2]
3[(5(c - 3d) +3(2c-5d)) (5(c - 3d) -3(2c-5d))]
3[(5c - 15d +6c-15d) (5c - 15d -6c+15d)]
3[-c(11c - 30d)]
-3c(11c - 30d)
3c (30d – 11c)

2. x^2 + 2xy + y^2 - x – y
    (x+y)(x+y) –1(x+y)
    (x +y)(x + y -1)

3. (x - 10)^2 - 5x
    x^2 – 20x +100 – 5x
    x^2 – 25x +100 
    (x – 20)(x – 5)

4. (a+b)^3 + (a - b)^3
    a^3 +3a^2b + 3ab^2 + b^3 + a^3 -3a^2b + 3ab^2 - b^3
    2a^3 + 6ab^2 
    2a (a^2 + 3b^2)

5. (a) 1 - 6t^2 + 9t^4
        9t^4 - 6t^2 + 1
        (3t^2 + 1) (3t^2 - 1)

(b) 1 - 6t^2 + 9t^4 - 121s^2
     9t^4- 6t^2 + 1 – 11^2s^2
     (3t^2 – 1)^2 – (11s)^2
     (3t^2 – 1 +11s) (3t^2 – 1 -11s)

6 .(a) -3x^2 - x + 2
         (2 – 3x)(1 +x)

Using the result of (a), factorize -3(2y + 1)^2 - (2y + 1) + 2
-3(2y + 1)^2 - (2y + 1) + 2
[2 – 3(2y +1)] [1 + (2y+1)]
[2 – 6y - 3] [1 + 2y +1]
[ – 6y - 1] [2y +2]
-2[ 6y + 1] [y +1]

7. If x^2 + cx + 16 can be factorized, write down 4 possible values of c.

c = 17, c = 10, c = 8, c = -8