(A) Factor: 8x²-2xy-1y²
Multiply the 8 by the 1 ignoring signs. Get 8
Write down all the ways to have two positive integers
which have product 8, starting with 8*1
8*1
4*2
Since the last sign in 8x²-2xy-1y² is -, SUBTRACT them,
and place the DIFFERENCE out beside that:
8*1 8-1=7
4*2 4-2=2
Now, again ignoring signs, we find in that list of
differences the coefficient of the middle term in 8x²-2xy-1y²
So we replace the number 2 by 4-2
8x²-2xy-1y²
8x²-(4-2)xy-1y²
Then we distribute to remove the parentheses:
8x²-4xy+2xy-1y²
Factor the first two terms 8x²-4xy by taking out the
greatest common factor, 4x, getting 4x(2x-y)
Factor the last two terms +5x-10 by taking out the
greatest common factor y, getting +y(2x-y)
So we have4
4x(2x-y)+y(2x-y)
Notice that there is a common factor, (2x-y)
4x(2x-y)+y(2x-y)
which we can factor out leaving the 4x and the +y to put
in parentheses:
(2x-y)(4x+y)
Edwin
