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# Algebra 1 Point 7

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### Algebra 1 Point 7

1. 1. 1.7 Combining Like Terms <ul><li>Objectives: </li></ul><ul><li>To simplify expressions by combining like terms </li></ul><ul><li>Frameworks: 10.P.3, 10.P.4 </li></ul>
2. 2. How could you simplify <ul><li>5b – 2b + 3b </li></ul><ul><li>6b </li></ul><ul><li>You don’t know what b equals, but that’s ok, it is simplified </li></ul><ul><li>This is called combining like terms . </li></ul>
3. 3. Fun examples from Trig . . . <ul><li>(3+5i)(9+4i) </li></ul><ul><li>= 3(9+4i) + 5i(9+4i) ( associative) </li></ul><ul><li>= 27 + 12i + 45i + 20i 2 </li></ul><ul><li>= 27 + 57i + 20i 2 </li></ul><ul><li>What does i stand for? </li></ul><ul><li>Because i = sqrt(-1), i 2 = -1 </li></ul><ul><li>= 27 – 20 + 57i </li></ul><ul><li>= 7 + 57i </li></ul>
4. 4. More fun from Trig . . . <ul><li>(7+2i)(7-2i) </li></ul><ul><li>7(7-2i) + 2i(7-2i) </li></ul><ul><li>49 +14i -14i - 4i 2 </li></ul><ul><li>= 49 - -4 </li></ul><ul><li>= 53 </li></ul>
5. 5. OK, back to Algebra <ul><li>The expression 7x +13xy 2 + 18 has 3 terms . </li></ul><ul><li>The term 18, with no variable, is called a constant term , or a constant . </li></ul><ul><li>Like terms have the same variables and the corresponding variables have the same exponents. </li></ul>
6. 6. Are these like terms? <ul><li>6x and 4x </li></ul><ul><li>7a 2 b and (1/2)a 2 b </li></ul><ul><li>5x and 5y </li></ul><ul><li>8t and 8 </li></ul><ul><li>3 and 2.7 </li></ul><ul><li>3m 2 n and 2mn </li></ul>
7. 7. Try some . . . <ul><li>8y – 3y </li></ul><ul><li>9a + 4b + 3a +5 </li></ul><ul><li>8y + y – 3y </li></ul>
8. 8. Try some . . . <ul><li>9 + 3(4a + 2) + a </li></ul><ul><li>9 + 12a + 6 + a Distribute & Multiply </li></ul><ul><li>9 + 6 + 12a + a Group like terms </li></ul><ul><li>15 + 13a Combine like terms </li></ul>
9. 9. Do p. 28 1-15