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# Algebra 6 Point 1

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### Algebra 6 Point 1

1. 1. 6.1 Multiplying Monomials<br />Objective: <br /><ul><li>To multiply monomials</li></ul>Frameworks: 10.P.1, 10.P.7<br />
2. 2. What is 36?<br />36 = 3 * 3 * 3 * 3 * 3 * 3<br />How else can we look at 36?<br /> 36 = (3 * 3) * (3 * 3 * 3 * 3) =32 * 34 <br /> 36 = (3 * 3 * 3) * (3 * 3 * 3) = 33 * 33 <br /> 36 = (3 * 3 * 3 * 3 * 3) * 3 = 35 = 31 <br />What is the pattern?<br />
3. 3. What is a monomial?<br />A monomial is either a constant, a variable, or a product of a constant and one or more variables:<br />Constants: 1 -3 ⅓ 5.2<br />Variables: x k a<br />Product: 4x3 -5xy πr2 (⅛)x<br />NOT a monomial: a2 + b2<br />
4. 4. Multiplying Monomials<br />The monomials a3 and a4 have the same base a but different exponents, 3 and 4.<br />To multiply a3 and a4, we add the 3 and the 4:<br />a3 * a4 = (a*a*a)*(a*a*a*a) = a3+4 = a7<br />
5. 5. Product of Powers<br />For all real numbers b and all positive integers m and n, <br />bm * bn = bm+n<br />
6. 6. Try some:<br />r7 * r<br />c2 * d2<br />x4 * y6<br />a2 * a3<br />
7. 7. What about (-3c2d)(7cd3)?<br />Use the commutative and associative properties of multiplication to group the constant coefficients together and the like bases together:<br />(-3*7)*(c2*c)(d*d3)<br />-21c3d4<br />
8. 8. Try some: <br />(-5x2y)(-xz3)<br />x2y(x2y2)<br />Evaluate for x = -3 and y = -1<br />
9. 9. Try some: <br />(3a5b4c)(-2b3c8)<br />(xy3)(x2y3)<br />Evaluate for x = -5 and y = 2<br />
10. 10. Turn to page 202<br />Do 1-12<br />