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8 1 Multiplying Monomials


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algebra 1 intro to monomials

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8 1 Multiplying Monomials

  1. 1. 8-1 Multiplying Monomials (sounds like some sort of disease, doesn’t it???)
  2. 2. What is a MONOMIAL? <ul><li>A monomial can be defined as: </li></ul><ul><li>a number (by itself, known as a constant) </li></ul><ul><li>a variable, or </li></ul><ul><li>the product of a number and a variable </li></ul><ul><li>( any expression involving the DIVISION of variables is NOT a monomial!) </li></ul>
  3. 3. Determine if the following are monomials: <ul><li>-3x 2 y </li></ul><ul><li>11 </li></ul><ul><li>3m + 4n </li></ul><ul><li>xyz </li></ul><ul><li>4h / 3j </li></ul>
  4. 4. The parts of a monomial <ul><li>coefficient </li></ul><ul><li>3m² exponent </li></ul><ul><li>base </li></ul>
  5. 5. Product of POWERS <ul><li>To multiply two powers that have the same base, ADD the exponents: </li></ul><ul><li>m ² • m³ = m 5 </li></ul><ul><li>To multiply two monomials that have the same base, with coefficients: multiply BIG, add LITTLE: </li></ul><ul><li>( 5x )( 2x ² ) = 10x ³ </li></ul><ul><li>*Don’t forget that variables without an exponent are understood to have a power of 1!! </li></ul>
  6. 6. Let’s try something harder! <ul><li>How about this one? </li></ul>
  7. 7. DON’T PANIC!! <ul><li>JUST FOLLOW THE RULES AND GO ONE STEP AT A TIME! </li></ul><ul><li>FIRST, MULTIPLY ALL OF THE COEFFICIENTS TOGETHER: </li></ul><ul><li>- 5 · 3 · 2/5 = - 6 </li></ul><ul><li>THEN, ADD UP THE EXPONENTS ON THE VARIABLES: </li></ul><ul><li>THERE ARE X’S AND Y’S TO COUNT UP: HOW MANY X’S ARE THERE? HOW MANY Y’S ARE THERE? </li></ul><ul><li>YOU SHOULD GET: x 5 y 6 </li></ul><ul><li>SQUASH THEM TOGETHER, AND YOUR ANSWER IS -6 x 5 y 6 </li></ul>
  8. 8. Power of a Power <ul><li>To raise a power to a power, </li></ul><ul><li>you MULTIPLY the exponents: </li></ul><ul><li>(x ³)² = x 6 </li></ul><ul><li>If there is a constant involved, </li></ul><ul><li>don’t forget to raise it to the power as well! </li></ul><ul><li>(2m²) 4 = 16m 8 </li></ul>
  9. 9. Power of a Product: <ul><li>Raise each factor to that same power </li></ul><ul><li>(2x 3 y 4 ) 5 = 32x 15 y 20 </li></ul><ul><li>(now that’s POWERFUL!) </li></ul>
  10. 10. Putting it all together: <ul><li>Simplify the following, </li></ul><ul><li>using the rules we have just covered: </li></ul><ul><li>2 x 5 y 4 (2 x 3 y 6 ) 5 </li></ul><ul><li>(4 x 2 y ) (2 xy 2 z 3 ) 3 </li></ul>
  11. 11. Applications <ul><li>GEOMETRY: Express the area </li></ul><ul><li>of this circle as a monomial. </li></ul><ul><li>Area = π r 2 (Formula for the area of a circle) </li></ul>
  12. 12. More applications <ul><li>Find the volume of the rectangular solid: </li></ul><ul><li>Volume of a rectangular solid: l •w•h   </li></ul>