8m^2- 34m - 98m2−34m−9
We can Split the Middle Term of this expression to factorise it:
In this technique, if we have to factorise an expression like am^2 + bm + cam2+bm+c, we need to think of 2 numbers such that:
N_1*N_2 = axxc = 8xx(-9)= -72N1⋅N2=a×c=8×(−9)=−72
And,
N_1 +N_2 = b = -34N1+N2=b=−34
After trying out a few numbers we get N_1 = -36N1=−36 and N_2 =2N2=2
(-36) xx 2 = -72(−36)×2=−72, and -36 +2 = -34−36+2=−34
8m^2- 34m - 9 = 8m^2- 36m + 2m - 98m2−34m−9=8m2−36m+2m−9
= 4m(2m - 9) + 1(2m - 9)=4m(2m−9)+1(2m−9)
= (4m + 1) (2m - 9) =(4m+1)(2m−9)
color(green)((4m + 1) (2m - 9) )(4m+1)(2m−9) is the Factorised form of 8m^2- 34m - 98m2−34m−9
