Question

Hey guys.. Please, I need your help right now. This is for tomorrow morning. ASAP

a(x) = (3x+1)(5x-4)-(x-12)(3x+1)-9x^2 + 1
b(x) = (4x+5)^2 - (2x-3)^2
A) Factorise a(x) and b(x)


Please, Help ASAP.

Show Your Work :)
Thanks

Answer 1

remember
a^2-b^2=(a-b)(a+b)

a.
ok so look at last bit

-9x^2+1
can be rearanged into
1-9x^2
look familiar?
1^2-(3x)^2
(1-3x)(1+3x) or
(1-3x)(3x+1)
we nowhave
(3x+1)(5x-4)-(x-12)(3x+1)+(1-3x)(3x+1)
factor out (3x+1)
(3x+1)(5x-4-(x-12)+1-3x)
(3x+1)(2x-3-x+12)
(3x+1)(x+9)


b.
easy

a^2-b^2=(a-b)(a+b)
(4x+5)^2-(2x-3)^2=
(4x+5-(2x-3))(4x+5+2x-3)=
(4x+5-2x+3)(6x+2)=
(2x+8)(6x+2)
we can factor out the 2 from each
(4)(x+2)(3x+1)


a(x)=(3x+1)(x+9)
b(x)=(4)(x+2)(3x+1)