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)(2x - 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
<=> \(\left[3x+1-2\left(x-2\right)\right]\left[3x+1+2\left(x-2\right)\right]\)
<=> (3x + 1 - 2x + 4)(3x + 1 + 2x - 4)
<=> (x + 5)(5x - 3)
e. 9(2x + 3)2 - 4(x + 1)2
<=> \(\left[3\left(2x+3\right)\right]^2-\left[2\left(x+1\right)\right]^2\)
<=> \(\left[3\left(2x+3\right)-2\left(x+1\right)\right]\left[3\left(2x+3\right)+2\left(x+1\right)\right]\)
<=> (6x + 9 - 2x - 2)(6x + 9 + 2x + 2)
<=> (4x - 7)(8x + 11)
f. 4b2c2 - (b2 + c2 - a2)2
<=> (2bc)2 - (b2 + c2 - a2)2
<=> (2bc - b2 + c2 - a2)(2bc + b2 - c2 + a2)
g. (ax + by)2 - (ay + bx)2
<=> (ax + by - ay - bx)(ax + by + ay + bx)
h. (a2 + b2 - 5)2 - 4(ab +2)2
<=> \(\left[a^2+b^2-5-2\left(ab+2\right)\right]\left[a^2+b^2-5+2\left(ab+2\right)\right]\)
<=> (a2 + b2 - 5 - 2ab - 4)(a2 + b2 - 5 + 2ab + 4)
<=> (a2 + b2 - 9 - 2ab)(a2 + b2 - 1 + 2ab)
i. (4x2 - 3x - 18)2 - (4x2 + 3x)2
<=> (4x2 - 3x - 18 - 4x2 - 3x)(4x2 - 3x - 18 + 4x2 + 3x)
<=> (-6x - 18)(8x2 - 18)
k. 9(x + y - 1)2 - 4(2x + 3y + 1)2
<=> \(\left[3\left(x+y-1\right)\right]^2-\left[2\left(2x+3y+1\right)\right]^2\)
<=> \(\left[3\left(x+y-1\right)-2\left(2x+3y+1\right)\right]\left[3\left(x+y-1\right)+2\left(2x+3y+1\right)\right]\)
<=> (3x + 3y - 3 - 4x - 6y - 2)(3x + 3y - 3 + 4x + 6y + 2)
<=> (-x - 3y - 5)(7x + 9x - 1)
l. -4x2 + 12xy - 9y2 + 25
<=> -(-4x2 + 12xy - 9y2 + 25)
<=> 4x2 - 12xy + 9y2 - 25
<=> (2x)2 - 2x . 3y . 2 + (3y)2 - 52
<=> (2x - 3y)2 - 52
<=> (2x - 3y - 5)(2x - 3y + 5)
m. x2 - 2xy + y2 - 4m2 + 4mn - n2
<=> (x2 - 2xy + y2) - \(\left[\left(2m\right)^2-2.2m.n+n^2\right]\)
<=> (x - y)2 - (2m - n)2
<=> (x - y - 2m + n)(x - y + 2m - n)
a: \(\left(3x-1\right)^2-16\)
\(=\left(3x-1-4\right)\left(3x-1+4\right)\)
\(=3\left(x+1\right)\left(3x-5\right)\)
b: \(\left(5x-4\right)^2-49x^2\)
\(=\left(5x-4-7x\right)\left(5x-4+7x\right)\)
\(=-8\left(3x-1\right)\left(x+2\right)\)
c: \(\left(2x+5\right)^2-\left(x-9\right)^2\)
\(=\left(2x+5-x+9\right)\left(2x+5+x-9\right)\)
\(=\left(x+14\right)\left(3x-4\right)\)
