I am stuck with these question on algebra factorisation
I mean i dun know how to factorise them. I will appreciate if you can provide me with the working and method. Thanks
1. (2a + 1)^3 + 2(2a + 1)^2 +2a + 1
Answer key for 1 is 4(2a +1)(a +1)^2, i got 4(2a^3 + 5a^2 +4a +1) at i am stuck...
2. (p + q)^2 + 2(p +q)(p -2q) + (p -2q)^2
Answer key for 2 is (2p - q)^2
nvm i had figured out the solution...
1.
(2a + 1)³ + 2(2a + 1)² + 2a + 1
(2a + 1)³ + 2(2a + 1)² + (2a + 1)
let b = 2a + 1
so it becomes:
b³ + 2b² + b
= b(b² + 2b + 1)
= b(b + 1)²
= (2a + 1)(2a + 1 + 1)²
= (2a + 1)(2a + 2)²
= (2a + 1)(2)²(a + 1)²
= 4(2a + 1)(a + 1)²
2.
(p + q)² + 2(p + q)(p - 2q) + (p - 2q)²
let p + q = a, p - 2q = b
so it becomes:
a² + 2ab + b²
= (a + b)²
= (p + q + p - 2q)²
= (2p - q)²