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## 4.3 Multiplying Monomials

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**4.3 Multiplying Monomials**Objectives: To apply laws of exponents to multiply monomials To extend these rules to more complicated monomials**Rules for Combining Like Terms**Recall that there are two requirements for being able to COMBINE LIKE TERMS • Same variables • Same exponents**Rules for Combining Like Terms**Alien Code #1: To ride in the same spaceship, you must have • Same BODY • Same NUMBER OF HEADS**Rules for Combining Like Terms**Alien Code #1: To ride in the same spaceship, you must have • Same BODY • Same NUMBER OF HEADS Leave variables alone Add the coefficients**3X2 + 1Y3 + 3Z4 +**2X2 + 1Y3 + 2X2 + 3Y3 + 1Z4 7X2 + 5Y3 + 4Z4 Leave variables alone Add the coefficients**Let’s try it with some more complicated monomials**3x2y3z4 + 5xy3z4 - 2x2y3z4 + 3xy3z4 1x2y3z4+ 8xy3z4 Leave variables alone Add the coefficients**Rules for Multiplying Monomials**Let’s extend this now to apply to when we multiply monomials • Multiply coefficients together • For exponents with same base (variable), add the exponents together**Rules for Multiplying Monomials**Alien Code #2: If aliens bump into each other, you have to • MULTIPLY the coefficients • Squish them into the same BODY • ADD the NUMBER OF HEADS**X2 TIMESX2**X4**Rules for Multiplying Monomials**Let’s extend this now to apply to when we multiply monomials • Multiply coefficients together • For exponents with same base (variable), add the exponents together X2 TIMESX2 X*X TIMES X*X X*X*X*X X4**34**3X2 TIMES4X2 (3)(4) 12X4**Examples**Simplify • (5x2)(-2x2) • (-3x3)(3x4) • (2y3)(3y4)**Multiplying Monomials**(-3x3y2z5)(3x2y3z) -9x • MULTIPLY the coefficients • Squish them into the same BODY**Multiplying Monomials**(-3x3y2z5)(3x2y3z) -9x5 • MULTIPLY the coefficients • Squish them into the same BODY • ADD the NUMBER OF HEADS**Multiplying Monomials**(-3x3y2z5)(3x2y3z) -9x5y • MULTIPLY the coefficients • Squish them into the same BODY**Multiplying Monomials**(-3x3y2z5)(3x2y3z) -9x5y5 • MULTIPLY the coefficients • Squish them into the same BODY • ADD the NUMBER OF HEADS**Multiplying Monomials**(-3x3y2z5)(3x2y3z) -9x5y5z • MULTIPLY the coefficients • Squish them into the same BODY**Multiplying Monomials**(-3x3y2z5)(3x2y3z1) -9x5y5z6 • MULTIPLY the coefficients • Squish them into the same BODY • ADD the NUMBER OF HEADS**Examples**Simplify • (5x2y3)(3x2y4) • (-3x3y2z5)(3x2y3z) • (2x2y3z3)(3x2y4)