Question 93561: Factor completeley
10a^2+ab-2b^2
Answer by checkley75(3666)   (Show Source):
You can put this solution on YOUR website! YOU NEED TO FIND A SET OF FACTORS FROM THE NUMBERS 10 &-2 THAT WNEM MULTIPLIED TOGETHER AND THEN ADDED WILL=1.
FACTORS FOR 10=1&10,-1&-10,2&5,-2&-5.
FACTORS FOR -2=1&-2,-1&2.
THESE ARE ALL POSSIBLE FACTORS.
NOW SELECT ONE FACTOR FROM EACH GROUP & MULTIPLY IT BY ONE FACTOR FROM THE OTHER SET & ADD THE PRODUCTS. WHEN YOU GET A SUM OF 1 THEN YOU HAVE THE ANSWER.
1*1+10*-2=1-20=-19 IS NOT A GOOD CHOICE.
2*-1+5*2=-2+10=8 IS NOT A GOOD CHOICE.
5*1+2*-2=5-4=1 LOOKS LIKE A WINNER.
NOW USEING THE OUTER & INNER ITEMS OF THE FOIL PROCEDURE WE GET:
OUTER=5*1=5 INNER=-2*2-4 NOW ADD 5-4=1 THE MIDDLE TERM OF THE EQUATION.
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10a^2+ab-2b^2
(5a-2b)(2a+b)
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