5 3w. Unit 2 Function Operations and Equivalence Standard 4.1 Add, Subtract, & Multiply Polynomials
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1 Unit Function Operations and Equivalence This document is meant to be used as an eample guide for each of the skills we will be holding students accountable for with Standard 4.1. This document should be viewed in conjunction with the 4.1 Skill List document. Skill 4.1 A - Identify like terms. (We cannot add or subtract polynomials if we cannot identify the like terms.) 1. List the pairs of like terms from the set of given terms.,,,, 0., 6,, -6, 0. The first pair are like terms because they are both constant terms, which means that they are not attached to any variables. The second pair are like terms because the numbers are attached to the eact same variable,. The third pair are like terms because the numbers are attached to the eact same variable,.. Identify the pairs of like terms in the polynomial , -, In the first pair it is important to note that the minus sign in front of the - term is the same thing as a negative sign. This is because subtracting a number is the same as adding the opposite of the number. For eample, 1 is the same as 1 + (-). We MUST include the sign in front of the term. Both of the terms in the second pairing are positive numbers as determined by the + signs in front of their terms in the polynomial. The last thing to note is that there are two other terms that are singletons, and have no like counterpart. Skill 4.1 B Add and subtract like terms. 1. Simplify. w w We combine the like terms (w w) and rewrite the epression as w or w.. Simplify We combine the like terms ( - ) and (+), and then you simplify the epression. Variable epressions are normally written with the terms in order of decreasing eponents such as However, the same epression can be rewritten in other ways so it is important to make sure that the plus (positive) and minus (negative) signs are correct. Students can rearrange variable epressions as they work them out. One option with specific steps is shown on the net page. Algebra 1 Parkway Central High School p.1
2 Unit Function Operations and Equivalence Original epression Group like terms together 14 Rearragne terms into decreasing power order. Skill 4.1 C Add polynomials. 1. Simplify. ( + ) + ( 4 7) Adding polynomials is very similar to adding and subtracting like terms. The original parenthesis used are just to indicate the two separate polynomial epressions. Solve by grouping together the like term pairs and then simplifying. ( + ) + ( ) 4 7 Original epression Rewrite without parenthesis (adding does not change any signs) Group like terms together. Simplify. ( + ) + ( + 8) + ( 4 + 1) Adding polynomials is very similar to adding and subtracting like terms. The original parenthesis used are just to indicate the two separate polynomial epressions. Solve by grouping together the like term pairs and then simplifying. ( + ) + ( + ) + ( + ) Original epression Rewrite without parenthe Group like terms together sis Skill 4.1 D Subtract polynomials. 1. Simplify. ( 1) ( + 4) There is one very important thing to remember when doing these problems you must subtract every term in the polynomial that is being subtracted, in this case, the second polynomial. There are various ways to attempt this but one of the most basic is to write the subtraction symbol over and over again as needed. Algebra 1 Parkway Central High School p.
3 Unit Function Operations and Equivalence ( ) ( + ) 1 4 Original epression Rewrite without parenthesis and remember to subtract each term of the second polynomial (this changes the sign of each term in the second polynomial.) Group like terms + 4 Skill 4.1 E Multiply by distributing a constant term. 1. Simplify. ( + ) Use the distributive property to rewrite the epression and then simplify to get + 6. ( + ) Original epression + Use the distributive property to multiply each inside term by the outside term + 6 Simplify. Simplify. ( + 1) Use the distributive property to rewrite the epression and then simplify to get -1. ( ) ( ) + 1 Original epression + 1 Use the distributive property. The parenthesis is added around the second negative three to emphasize and help remember its' sign. 1 + Simplify both multiplication steps 1 Rewrite the multiple signs (adding a negative is the same as subtracting.) Skill 4.1 F Multiply by distributing a variable epression. 1. Simplify ( + ) Use the distributive property to rewrite the epression and then simplify to get +. When we multiply times, we get.. Simplify ( 4) Use the distributive property to rewrite the epression and then simplify to get Original equation. ( ) 4 Distribute the outside term. times is Simplify. Algebra 1 Parkway Central High School p.
4 Unit Function Operations and Equivalence Skill 4.1 G Multiply by distributing a binomial into a binomial. 1. Simplify ( )( ) +. ( + )( ) ( ) + ( ) 6 + Original epression Split up the first term into two parts 1 Distribute both parts 1 Combine like t. Simplify ( + 6)( 4 1) ( + 6)( ) ( ) + 6( ) erms 4 1 Original epression Split apart the first term + Distribute both parts Simplify Skill 4.1 H Perform multiple operations distribute and then add or subtract polynomials 1. Simplify ( + ) 4( 1) ( + ) ( + ) ( ) ( + ) 4 1 Original epression Distribute the first and second terms and then Combine like terms subtract both parts of the third paranthesis. Skill 4.1 I Multiply by distributing a binomial into a trinomial. 1. Simplify ( + )( 4 + 6) ( + )( + ) ( + ) + ( + ) 4 6 Original epression Split apart the first paranthesis and distribute Combine li ke terms Algebra 1 Parkway Central High School p.4
5 Unit Function Operations and Equivalence Skill 4.1 J Perform multiple operations square a binomial 1. Simplify ( + ) ( + ) ( + )( + ) Original epression Rewrite Multiply the binomials Skill 4.1 K Simplify epressions using properties of eponents 1. Simplify When dividing the same base, you subtract the eponents. =. Simplify y Each part of the fraction can be rewritten. = y y. Simplify ( y ) 6 When there are eponents inside and outside a parenthesis, you multiply the eponents. ( ) 6 y = y Simplify 0 y Any non-zero number raised to the power of zero equals one. y = 1 y = y 0. Simplify A negative eponent is rewritten as a positive eponent by moving the 1 base to the bottom of a fraction. = Practice for the epert level items can be received from the teacher. Students are able to check out a book for practice if needed. Algebra 1 Parkway Central High School p.
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