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Math Asked by a SnapAndSolve user · 21 minutes ago

JUSTIFY WHY: Show all work. Complete each product table using monomials. Then write the product for each...

1. JUSTIFY WHY: Show all work.
Complete each product table using monomials. Then write the product for each table as a polynomial in standard form.
2. JUSTIFY WHY: Show all work.
Find the area of the rectangle.
(2x + 5) yards
(2x - 5) yards
The area of the rectangle is
Choose equation
Choose unit

Answer

  1. Product Table: Multiply each term in the first binomial by each term in the second binomial. For example, if the binomials are (x + 4) and (x - 5), the product is:

    x * x = x²
    x * (-5) = -5x
    4 * x = 4x
    4 * (-5) = -20

    Polynomial in Standard Form: Combine like terms:
    x² - 5x + 4x - 20 = x² - x - 20

  2. Area of the Rectangle: Use the formula for the area of a rectangle, which is length × width.

    Area = (2x + 5)(2x - 5)

    Use the distributive property (FOIL method):
    (2x + 5)(2x - 5) = 2x(2x) + 2x(-5) + 5(2x) + 5(-5)
    = 4x² - 10x + 10x - 25
    = 4x² - 25

    The area of the rectangle is: 4x² - 25 square yards

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