Sign of first entry should be positive; otherwise, factor out a (-1)
Also factor out any common numbers from the entire equation
20x2 + 7xy - 3y2
Drop the 20 to both sets of parenthesis
(20x )( )
(20x )(20x )
Drop the 1st sign (from the middle entry) to the first parenthesis
(20x + )(20x )
Multiply the 1st sign (from the middle entry) by the last sign,
then drop the resulting sign into 2nd set of parenthesis
(20x + )(20x - )
Multiply the 1st and 3rd numbers which gives us 60.
Find 2 numbers that multiply together to give 60
and that subtract (based on last sign) to give the
middle entry.
20*3=60
1*60
2*30
3*20
4 *
5*12
12 - 5 = 7
6*10
7 *
8 *
9 *
Drop the larger number in the first parenthesis
(20x + 12y)(20x - )
Drop the smaller number in the second parenthesis
(20x + 12y)(20x - 5y)
Since you've already factored out any common factors at
the beginning we just factor out any common numbers out
of each parenthesis set and throw them away.
(20x + 12y)(20x - 5y)
4(5x + 3y)(20x - 5y)
4(5x + 3y)5(4x - y)
(5x + 3y)5(4x - y)
(5x + 3y)(4x - y)
9x2 - 6xy + y2
(9x )(9x )
(9x - )(9x )
(9x - )(9x - )
[- * + = -]
9 * 1 = 9
[1st number multiplied by last number]
What factors of 9 added (last sign) together equal 6 (middle value)
1 * 9 = 9
3 * 3 = 9
[3 + 3 = 6]
(9x - 3y)(9x - 3y)
Larger in 1st parenthesis, smaller in 2nd parenthesis.
Now factor and discard
(9x - 3y)(9x - 3y)
3(3x - 1y)(9x - 3y)
(3x - 1y)(9x - 3y)
(3x - 1y)3(3x - 1y)
(3x - 1y)(3x - 1y)
(3x - y)(3x - y)