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Name: Date: VARIABLES, Tums, AND EXPRESSIONS COMMON CORE ALGEBRA II Homwonx FLUENCY 1. For each of the following expressions, state the number of terms. (a) 3x2 -1 (b) 8x+?x' -2+x3 (e) "my2:33,: +%xy' 2. Simplify each of the following expressions by combining like terms. Be careful to only combine terms that have the same variables and powers. (a) 2x2 +3xl+5x22.r3 (b) Sx22x+10x2+?x+5 (c) 41:23; 21y2 +911:2 x2y [d] 71:2 2x2y+4xy2 3:3 +2}:2 +9x2y +143;3 3. Given the algebraic expression 12:12 do the following: x _ (3) Evaluate the expression for when x = 7 _ (b) Evaluate the expression for when x = 4 _ (c) Nina believes that this expression is equivalent to dividing 12 by one less than it. Do your results from (a) and (b) support this assertion? Explain; 4. Classify each of the following as either a monomial (single term), a binomial (two terms) or a trinomial {three terms). (a) 4x1 (b) 3x'+2x1 (C) 1613 {a} x=y1+2s (e) (r) mum4:2 5. Use the distributive property rst and then combine each of the following linear expressions into a single, equivalent binomial expression. {a} S(21+3)+2[4xI] (b) 2(Ix+1)3(4x-5) 6. Which of the following is equivalent to the expression 2(x 6}+ 4(2x+1)+ 3 ? {1) 8(x2) (3) 4(2x+3) {2) 5(211) (4) [0(xl) Rsssosmo 7. Each step in simplifying the expressions you worked with in 5 and 6 can be justied using one of the major properties of real numbers reviewed in the lesson. Justify each step below with either the commutative, associative or distributive propertiu when simplifying the expression 8(31 + 1] + 2 (5x+ T) . S(3x+l)+2(5x+?) = 24x+8+lx+l4 =24x+10x+3+l4 =(24x+le}+(8+14) = x(24+10)+22 = 341+ 22