First, determine the sign, then multiply the numerical coefficients, next multiply the literalcoefficients, and finally, multiply these two products together. Follow this example so that youcan understand each step as it is performed.Examples: Determine sign = Numerical values = Literal values = Product = Using the four steps in the example, find the product of each equation in the following challenge.1-53(+)&(-29 =(-3x&-5xy=3&-5= -15x&x&y=x2y-15x2y(a)Distributive property(b)Associative property(c)Commutative property7(a+t29 =7a+7t3(xy29 = (3x29yIR=RI(Fill in the blank)Identify the term that best describes the expressions.(a)___________ ___________(b)___________ ___________(c)___________ ___________7(a+t29 =7a+7t3(xy29 = (3x29yIR=RI
If your answer to the challenge is the same as follows, you may continue. If you answered anyequation in the challenge incorrectly, review paragraph 1403 before continuing.You are now ready to multiply a polynomial by a monomial. Multiply each term of thepolynomial by the monomial using the distributive property. If you need to review the distributiveproperty, it was covered in paragraph 1402. As you can see in the following examples, writingthe product of each operation will help you maintain the appropriate signs.Examples:(a)1-544x(2m-3n)=4x(2m)-4x(3n)=8mx-12nx(a)(b)(c)(-7IR)(-12E2)=(-4a2b)(3bc2)=3x2y26xy2=(-)&(-)=(+)7&12=84I&R&E2=E2IR=84E2IR(-)&(+)=(-)4&3=12a2&b&b&c2=a2b2c2= -12a2b2c2(+)&(+)=(+)3&6=18x2&x&y2&y2=x3y4=18x3y4Find the products of the following monomial equations.(a)(b)(c)(-7IR)(-12E2)=(-4a2b)(3bc2)=3x2y26xy2
(b)Try the following challenge on finding the products of monomials and polynomials.If your answers to the challenge are the same as follows, you are correct and may continue. Ifyou answered any part of the challenge incorrectly, review paragraph 1403 before continuing.1-55(a)(b)(c)2x3x-2y-b(a2+ab+b2)2y4x2y+7xy+3y2=2x(3x)-2x(2y29=6x2-4xy= -b(a2)-b(ab)-b(b2)= -a2b-ab2-b3=2y4x2y+2y7xy+2y3y=8x2y2+14xy2+6y3Find the products of the following equations.(a)(b)(c)2x3x-2y=-b(a2+ab+b2)=2y4x2y+7xy+3y2=-9c(8c-9cL+3L)= -9c(8c)-(-9c)(9cL)+(-9c)(3L)= -72c2-(-81c2L)+(-27cL)= -72c2+81c2L-27cL
1404.Find Binomial ProductsYou can find a product for two binomials by using a procedure called the FOIL method. Theabbreviation FOIL provides a four step procedure to multiply binomials more efficiently. Youmultiply in this order, the first terms, the outer terms, the inner terms, the last terms, and then addthe resultant polynomial. In the example below, you can see the FOIL method step by step. Example:Ffirst terms Oouter terms Iinner terms Llast terms Note:If possible, you need to combine any like terms by algebraic addition.