9.PR.6 Adding and Subtracting Polynomial Expressions.pptx

Adding and Subtracting Polynomials

1. Adding and Subtracting Polynomial s Chapter 5.3 - Patterns and Relations Section Recall Adding Polynomial Expression Integer review: This is why the 2 green highlighted additions below change to subtraction, and why we get the same answer (because a (+) x (-) = (-...) (+) + (+) = additio n 3 + 4 = 7 (+) + (-) = subtraction 3 + (-4) = 3 - 4 = -1 (-) + (+) = addition -3 + 4 = 1 (-) + (-) = subtraction -3 + (-4) = -3 - 4 = -7 Ex/ Solve the following using multiplication to get rid of one sign, then combine the terms -3 + (-4) 2) 6x + (5x) 3) -3yr + (-4yr) What would happen for the following questions then??? (2x - 5) + (4x - 6) 2) (-4x - 2) + (-5x + 5) When we are adding polynomial expressions, all we are doing is combining like terms W hen we multiply by a positive to get rid of brackets before combining, we are multiplying EACH term in the second set of brackets by a positive, AND THERE IS NO SIGN CHANGE TO THE TERMS IN THE SECOND SET OF BRACKETS A shortcut is to ignore or remove the addition sign, as well as the brackets!!!

2. Adding Polynomials Chapter 5.3 - Patterns and Relations Section Two ways to Add Using a Model Try Use a Model - Algebra Tiles Combine Terms using Math Symbols Use the same process as when we used algebra tiles to combine like terms Get the amount of algebra tiles that represent each term Group the like tiles together Decide how many of each tile you are left with once you use the positives and negatives to cancel each other (One positive tile cancels one negative tile) Write the term that matches the amount of each type of algebra tile you have left Put the terms in order from GREATEST EXPONENT to LEAST EXPONENT to make your new simplified expression Add 3x - 4 and 2x - 5 using a model (algebra tiles) Can also look like (3x - 4) + (2x - 5)

3. Adding Polynomial Expressions cont. Using Math Symbols Try Use the same process as when we used math to combine like terms without using algebra tiles, EXCEPT we first get rid of brackets...this is where multiplication comes in: Use multiplication to get rid of brackets and write expression as one long polynomial instead of 2 individuals, (or just ignore the addition between the 2 polynomials and remove the brackets - it makes no difference!!!) Make shapes around like terms in an expression, or circle them with individual colors - remember the sign goes with term that follows it! List the like terms side by side Add THE COEFFICIENTS in each group of like terms to simplify and be left with only one term of each type...the variables and exponents do not change! Put the leftover terms side by side to make your new simplified expression in order from GREATEST EXPONENT to LEAST EXPONENT Add 3x - 4 and 2x - 5 Can also look like (3x - 4) + (2x - 5) 4) 5)

4. Adding Polynomial Expressions cont. Try Again

5. Opposite Expressions Recall Opposite Expression Try The opposite of a number is just the same number but with the opposite sign 3 is opposite of -3 -7 is opposite of 7 An opposite term or expression is one in which all positives have now been switched to negatives, and all negatives have now been switched to positives Don’t forget, that if there is no sign shown before the first term in an expression, it is a positive term and will become a negative in the opposite expression What is the opposite of each of the following terms/expressions? 3x b) -2 c) 4x - 1 d) a 2 - 3a + 2

6. Subtracting Polynomial Expressions Recall Subtracting Polynomial Expression When we are adding or subtracting integer terms, we also use multiplication to get rid of any brackets!!! When subtracting, we need to notice that when we multiply to get rid of brackets, we are multiplying EACH term in the second set of brackets by a negative, SO THERE WILL BE A SIGN CHANGE TO THE TERMS IN THE SECOND SET OF BRACKETS For this reason, we can’t just ignore the subtraction and remove the brackets as we did with addition Ex/ Solve the following using multiplication to get rid of one sign, then combine the terms -3 - (-4) 2) 6x - (5x) 3) -3yr - (-4yr) What would happen for the following questions then??? (2x - 5) - (4x - 6) 2) (-4x - 2) - (-5x + 5) What do you notice about the second set of terms once we have multiplied to get rid of brackets???

7. Subtracting Polynomial Expressions cont. To Subtract, We Add! Try ANOTHER WAY TO SAY THIS - Combine the opposite terms Use multiplication to get rid of brackets and write expression as one long polynomial instead of 2 individuals or just ignore the subtraction between the 2 polynomials, and change the second terms to their opposites before you remove the brackets ***The rest of the steps are now the same as for adding polynomial expressions*** Make shapes around like terms in an expression, or circle them with individual colors - remember sign goes with term after it! List the like terms side by side, KEEPING AN ADDITION SIGN BETWEEN THEM!!! ADD THE COEFFICIENTS in each group of like terms to simplify and be left with only one term of each type...the variables and exponents do not change! Put the leftover terms side by side to make your new simplified expression in order from GREATEST EXPONENT to LEAST EXPONENT What is left when you take 3x - 4 from 2x - 5 Can also look like (2x - 5) - (3x - 4) Why did the order change? 4) 5)

8. Subtracting Polynomial Expressions cont. Try Assigned Due: Next Class Simplify the following expressions: (2x - 3) - (-x + 2 ) b) (5x 2 - x + 4) - (2x 2 - 3x -1) Pg.196 #5-7, 8, 10, 12, 14, 15, 17, 19, 22, 16, 18, 20, 24 will be done together in class next day If the question asks you to model your solution, it means to show the answer by drawing algebra tiles Due: Next Class