1-6B Distributive Property and Combine Like Terms – Evaluate Algebraic Expressions Algebra 1 Glencoe McGraw-HillLinda Stamper

Do not use a calculator to complete homework. Students who are calculator dependent tend to make more calculating errors on tests. Don’t skip steps. Write out the support work so your eyes can see what your brain needs to calculate. “I did it in my head” often leads to errors. After you finish an odd homework problem check the answer in the back of the book. If the answer is incorrect, investigate why it is wrong. When students find their errors right away it is more effective. Study tips Take notes in class, read the related lesson in the text, and then review, review, review. It’s just not enough to sit in class for 45 minutes and then hope you have absorbed it all.

––3(m 5)+–+– The problem. A common error in distributing occurs when a negative is involved with subtraction. To avoid errors change subtraction to addition. Distribute. –3m + 15 –3m Simplify.  + – 3(–5) Change subtraction to addition. –3(m - 5)

–8(m 9) Rewrite using the distributive property. Then simplify. –8m + 72 –8m  + – 8(–9) –+–+– –8(m - 9) Example 1 (3g 8)(–5) Example 2 –15g g(–5)  + – 8(–5) –+–+– (3g - 8)(–5) –8(x 2y + 3z) Example 3 –8x + 16y + – 24z –8x+ – 8(–2y) –8x + 16y – 24z + – 8(3z) –+–+– –8(x - 2y + 3z) Note: Your answer must be simplified. Undo the double signs.

The problem. Rewrite using the distributive property. Then simplify. Give the negative sign a multiplier of 1. Simplify. Change subtraction to addition. What property justifies this step? 7y Copy in your spiral notebook!

– (m - 7) – (m 7) – (–2x 15)+–+– –(–2x - 15) Example 4 2x + 15 (–1)–2x  +(–1)(–15) – 1 Rewrite using the distributive property. Then simplify –+– – Example 5 –1(m)  + (– 1)(–7) –m+ – (6 y) +–+– – Example 6 –1(6)  + (– 1)(–y) – 6+ y Good form gives the variable term before the constant! What property justifies this move? 1 – (6 - y) Use good form! Do not write as -1m + 7.

Simplify the expression. Like terms are terms in an expression that have the same variable raised to the same power. An expression is simplified if it has: no grouping symbols, no like terms, and no double signs. In the answer, good form is alphabetical, descending order! Constants are last.

Please do not confuse these types of problems. x + x + x =3x x x x =x3x3 2x + 2x + 2x =6x 2x 2x 2x =8x 3 x x x

+ Write problem. 5x 2 7x + 3x 2 + 5x Simplify the expression. Change subtraction to addition. 8x 2 Combine like terms. 8x 2 – 2xUndo the double signs. +–+– – 8x 2 +(–2x) Good form is alphabetical descending order! Constants are last. – 2x

Example 7 Simplify the expression. Example 8 3(y + 6) + 5(4 - y) + 7y 2 Example 9 4y - (6y - 9) Example 10 a - b(b - 2a) + 4b 2

+ 38 3x 2 5x + 4x 2 7x –– Example 7 7x 2 7x 2 – 12x + – 12x +–+– +–+– Simplify the expression. 3(y + 6) + 5(4 y) + 7y 2 Example 8 – 2y 3y – 5y –+–+– + 7y 2 7y 2 Good form has the variables in alphabetical order with the powers in descending order! Constants are last. 3(y + 6) + 5(4 - y) + 7y 2 3(y)+3(6)5(4)+5(-y)++ 7y 2

+ 3b Simplify the expression. 4y (6y 9) Example 9 –2y Distribute the negative one. 4y + – 6y +9 +–+– –– +–+– 1 4y - (6y - 9) 4y + (-1)(6y) + (-1)(-9) a - b(b - 2a) + 4b 2 Good form is alphabetical descending order! +–+– a b(b 2a) + 4b 2 +–+– – Example 10 – a +a + – b 2 +2ab a+ 2ab + 4b 2 a + (-b)(b) +(-b)(-2a)+4b 2

simplified An algebraic expression is easier to evaluate when it is simplified. Simplify by using the distributive property and then combine like terms. Then use the value given to evaluate. Evaluating Algebraic Expressions

–5x(2 3x) + 7x+–+– Write the problem. Simplify and then evaluate when x = –2. Change subtraction to addition. –10x Distribute. + 15x 2 + 7x Combine like terms. – 3x +15x 2 Substitute (don’t forget to use parentheses). – 3(–2) +15(–2) 2 Simplify. 15(4) + (–3)(–2) – –5x(2 - 3x) + 7x

– x(8 x) + 2x+–+– Simplify and then evaluate. – 8x + x2x2 + 2x – 6x+x2x2 – 6(2)+(2) – 6(2) 4 + – 12 –8–8 – – x(8 - x) + 2x Example 11 when x = 2 +–+– 6( x 3) x(9 + x) – Example 12 when x = 4 – 6x + – 18 + – 15x + – 18 – 15(4)+ – 18 –16 + – 15(4) + – 18 – 16 + – 60 + – 18 –94 – 9x+ –x2–x2 +– x2– x2 +– (4) 2 +–+– –– 6(-x - 3) - x(9 + x) – 76 + – 18

1-A11 Handout A11