Question

part ii: using the foil method, multiply the terms in the binomials below. show your work in the blanks provided. then, add any like terms and write the polynomial in standard form in the space provided.show your work. (8 points: 2 points each)
a. (3x + 7)(2x - 5) b. (x² + 2x)(5x² - 3x)
c. (5x + 4)(5x - 4) d. (x² - 7)(x² - 4)

1. use the distributive property to multiply the trinomial by the binomial.

circle the first term in the trinomial, multiply it by each term in the binomial, and place each result inthe blank spaces provided. repeat this process for the second and third terms of the trinomial until allof the spaces are filled in. finally, in the space provided beneath the blanks, simplify the expression bycombining like terms and arranging the terms from highest to lowest order. show your work. (4 points)
(3x² - 2x + 7)(x² + 2x)

1. use the vertical method to multiply two trinomials.

Explanation:

Step1: Multiply each term of the trinomial by each term of the binomial

$$3x^{2}\times x^{2}+3x^{2}\times2x - 2x\times x^{2}-2x\times2x + 7\times x^{2}+7\times2x$$

Step2: Simplify each product

$$3x^{4}+6x^{3}-2x^{3}-4x^{2}+7x^{2}+14x$$

Step3: Combine like terms

$$3x^{4}+(6x^{3}-2x^{3})+( - 4x^{2}+7x^{2})+14x$$
$$3x^{4}+4x^{3}+3x^{2}+14x$$

Answer:

$$3x^{4}+4x^{3}+3x^{2}+14x$$