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Question 34316: Give an example of using the distributive property for a negative monomial times a trinomial with different signs on the terms [for example: -3x(2xy + 3y – 2x)] and show each step of the distribution. Why do you think many students make sign errors on this type of problem? What would be your advice to a student who has trouble with the signs?
Can you help me with this please?
Thank you
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! Give an example of using the distributive property for a negative monomial times a trinomial with different signs on the terms [for example: -3x(2xy + 3y – 2x)] and
THE RULE IS SIMPLE..+ * + = +....- * - = + AND - * + = - = + * - ...THAT IS PRODUCT IS POSITIVE IF BOTH ARE OF SAME SIGN ...AND NEGATIVE IF BOTH ARE OF DIFFERENT SIGNS...APPLYING IN THE ABOVE EXAMPLE,WE GET
+(-3X)(2XY)+(-3X)(3Y)+(-3X)(-2X)=-6X^2*Y-6XY+6X^2.....SEE COMMENTS BELOW...
show each step of the distribution. Why do you think many students make sign errors on this type of problem?
1.NEGLIGENCE..
2.LACK OF AWARENESS OF THE ABOVE RULE OF PRODUCT OF SIGNS....
3.NOT USING APPROPRIATE BRACKETS OR USING WRONG BRACKETS...THIS IS THE MOST ..IMPORTANT ASPECT TO BE REMEDIED.
4.NOT FOLLOWING A SYSTEMATIC PROCEDURE..THAT IS OMITTING STEP BY STEP APPROACH WITHOUT HAVING THE EXPERIENCE.YOU CAN JUMP STEPS OR OMIT STEPS IF YOU ARE EXPERIENCED.IF NOT YOU ARE BOUND TO MAKE MISTAKES.
What would be your advice to a
student who has trouble with the signs?
Can you help me with this please?
REMEDY THE ABOVE DFECTS...
1...THIS IS IN YOUR OWN HANDS
2...NOW YOU KNOW THE RULE.
3...SEE THE USE OF BRACKETS IN THE ABOVE EXAMPLE BY ME.THAT CLEARLY SHOWS THE PRIORITY OR ORDER OF EXECUTION OF OPERATIONS.
4.ONE SYSTEMATIC PROCEDURE FOR BEGINERS IS TO PUT + SIGN BETWEEN EVERY 2 TERMS OF EXPANSION WHILE USING DISTRIBUTIVE PROPERTY OF MULTIPLICATION OVER ADDITION OR SUBTRACTION.
SEE IN THE ABOVE EXAMPLE.I PUT ALL + SIGNS ONLY ,THOUGH THERE IS A MINUS SIGN IN FRONT OF 3X BEFORE THE BRACKETS TO START WITH AND ALSO IN THE LAST TERM WITHIN THE BRACKETS NAMELY -2X.THIS - SIGN WHEREVER IT IS PRESENT, IS PUT WITHIN BRACKETS TO START WITH.THEN WHEN BRACKETS ARE OPENED BY MULTIPLICATION,WE FIRST USED THE ABOVE RULE OF SIGNS TO DETERMINE THE SIGN OF THE ANSWER AND THEN THE VALUE OF THE ANSWER IS CALCULATED AND PUT.
BY USING THIS SYSTEMATIC 2 STEP APPOACH,TILL YOU GAIN EXPERIENCE, THOUGH IT IS LITTLE TIME CONSUMING, WILL AVOID MISTAKES.ONCE YOU GAIN EXPERIENCE YOU CAN SKIP THE STEPS AND PUT THE FINAL ANSWER.
LAST WARNING...BE VERY CAREFULL IF THERE ARE MULTIPLE BRACKETS..SEE BELOW..
-3[5-2{4-3(2-3)}]...HERE OPEN BRACKETS ONE BY ONE STARTING FROM INNERMOST FIRST
=-3[5-2{4-3*(-1)}]
=-3[5-2{4+3}]
=-3[5-2*7]
-3[5-14]
=-3*(-9)
=+27
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