How do you factor the expression #x^2 - 8x + 16#?

1 Answer
Jan 18, 2016

Answer:

#color(blue)(( x-4) (x-4)# is the factorised form of the expression.

Explanation:

#x^2-8x+16#

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like #ax^2 + bx + c#, we need to think of 2 numbers such that:

#N_1*N_2 = a*c = 1*16 =16#

AND

#N_1 +N_2 = b = -8#

After trying out a few numbers we get #N_1 = -4# and #N_2 =-4#
#-4*-4 = 16#, and #(-4)+(-4)= -8#

#x^2-color(blue)(8x)+16 = x^2-color(blue)(4x-4x)+16#

#= x(x-4) -4(x-4)#

#= color(blue)(( x-4) (x-4)#