`#040911`
`a)`
`196 - a^2 + 2ab - b^2`
`= 196 - (a^2 - 2ab + b^2)`
`= 196 - (a - b)^2`
`= 14^2 - (a - b)^2`
`= (14 - a + b)(14 + a - b)`
`b)`
`a^2 + 6a - 4b^2 + 9`
`= (a^2 + 6a + 9) - 4b^2`
`= [ (a)^2 + 2*a*3 + 3^2] - (2b)^2`
`= (a + 3)^2 - (2b)^2`
`= (a + 3 - 2b)(a + 3 + 2b)`
`c)`
`4x - 4 + 9y^2 - x^2`
`= 9y^2 - (x^2 - 4x + 4)`
`= (3y)^2 - [ (x)^2 - 2*x*2 + 2^2]`
`= (3y)^2 - (x - 2)^2`
`= (3y - x + 2)(3y + x - 2)`
`d)`
`5x^2 - 10x + 5 - 45t^2`
`= 5*(x^2 - 2x + 1 - 9t^2)`
`= 5*[ (x^2 - 2x + 1) - 9t^2]`
`= 5*{ [(x)^2 - 2*x*1 + 1^2] - (3t)^2}`
`= 5*[ (x - 1)^2 - (3t)^2]`
`= 5*(x - 1 - 3t)(x - 1 + 3t)`
`e)`
`x^2 - 36y^2t^2 - 10x +25`
`= (x^2 - 10x + 25) - 36y^2t^2`
`= [ (x)^2 - 2*x*5 + 5^2] - (6yt)^2`
`= (x - 5)^2 - (6yt)^2`
`= (x - 5 - 6yt)(x - 5 + 6yt)`
a: =196-(a^2-2ab+b^2)
=196-(a-b)^2
=(14-a+b)(14+a-b)
b: \(=\left(a^2+6a+9\right)-4b^2\)
\(=\left(a+3\right)^2-4b^2\)
\(=\left(a+3-2b\right)\left(a+3+2b\right)\)
c: \(=9y^2-\left(x^2-4x+4\right)\)
\(=\left(3y\right)^2-\left(x-2\right)^2\)
\(=\left(3y-x+2\right)\left(3y+x-2\right)\)
d: \(=5\left(x^2-2x+1-9t^2\right)\)
\(=5\left[\left(x-1\right)^2-\left(3t\right)^2\right]\)
\(=5\left(x-1-3t\right)\cdot\left(x-1+3t\right)\)
e: \(=x^2-10x+25-36y^2t^2\)
\(=\left(x-5\right)^2-\left(6yt\right)^2\)
\(=\left(x-5-6yt\right)\left(x-5+6yt\right)\)