a. (3x - 1)2 - 16
= (3x - 1)2 - 42
= (3x - 1 - 4)(3x - 1 + 4)
= (3x - 5)(3x + 3)
= 3(3x - 5)(x + 1)
b. (5x - 4)2 - 49x2
= (5x - 4)2 - (7x)2
= (5x - 4 - 7x)(5x - 4 + 7x)
= \(\left(-2x-4\right)\left(2x-4\right)\)
= 2(-x - 2) . 2(x - 2)
= 4(-x - 2)(x - 2)
c. (2x + 5)2 - (x - 9)2
= (2x + 5 - x + 9)(2x + 5 + x - 9)
= (x + 14)(3x - 4)
2.
a)(3x-1)2-16 = (3x-1)2-42
=(3x-1-4).(3x-1+4)= (3x-5).(3x+3)
b)(5x-4)2-49x2 =(5x-4)2-(7x)2
= (5x-4-7x).(5x-4+7x) = (-2x-4).(12x-4)
c)(2x+5)2-(x-9)2 =(2x+5-x+9).(2x+5+x-9) =(x+14).(3x-4)
d)(3x+1)2-4.(x-2)2 =(3x+1)2-[2.(x-2)]2 = [3x+1-2.(x-2)].[3x+1+2.(x-2)]
= (3x+1-2x+4).(3x+1+2x-4)
= (x+5).(5x-3)
e)9.(2x+3)2-4.(x+1)2 =[3.(2x+3)]2-[2.(x+1)]2
=[3.(2x+3)-2.(x+1)].[3.(2x+3)+2.(x+1)]
=(6x+9-2x-2).(6x+9+2x+2)
=(4x+7).(8x+11)
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