(4x+1)(4x-3)
The GCF is 8x.
(4x + 3y)(4x + 3y) or (4x + 3y)2
2x(8x-7)
4x3 + 16x2 - 180x = 4x(x2 + 4x - 45) = 4x(x + 9)(x - 5)
16x2 - 25 = (4x + 5) (4x - 5)
I think that wants to be 16x2 - 40xy + 25y2 That factors to (4x - 5y)(4x - 5y) or (4x - 5y)2
The difference of cubes has a formula. (4x - y)(16x2 + 4xy + y2)
16x2 - 25 = (4x + 5) ( 4x - 5)
You need to spot that 16x2 is the square of 4x and that 225 is the square of 15. Notice that the expression is a "difference of 2 squares", which is a standard result in algebra a2 - b2 = (a + b)(a - b) so here we factorise to (4x + 15)(4x - 15)
You can use the formula for the difference of two squares in this case. - In general, for factoring, check whether the expression to be factored corresponds to one of several common forms - as in this case.
The GCF is 2.
34-132
(4x-3)(4x+3)
(4x + 6)(4x - 6)
If that's 16x2 + 72x + 81, that factors to (4x + 9)(4x + 9) or (4x + 9)2
(4x+1)(4x-3)