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Difficulty: EasyOperations on Polynomials

A rectangle has a length of y+7y + 7 inches and a width of y−3y - 3 inches. Which of the following expressions represents the area, in square inches, of the rectangle?

  1. A
    y^2 - 21
  2. B
    y^2 + 4y + 21
  3. y^2 + 4y - 21Answer
  4. D
    y^2 - 4y - 21
  5. E
    5y - 21

Answer

The expression y2+4y−21y^2 + 4y - 21
The area of a rectangle is found by multiplying its length by its width. The product of the dimensions is represented by the expression (y+7)(y−3)(y + 7)(y - 3). Applying the distributive property gives y2−3y+7y−21y^2 - 3y + 7y - 21. Combining the like terms −3y-3y and 7y7y results in +4y+4y. Therefore, the simplified expression for the area is y2+4y−21y^2 + 4y - 21.

Step-by-Step Solution

1
Set up the area formula for the rectangle by multiplying its length and width.
Area =(y+7)(y−3)= (y + 7)(y - 3)
The area of a rectangle is calculated by multiplying its length by its width.
2
Use the distributive property to expand the product of the two binomials.
Area =y(y)+y(−3)+7(y)+7(−3)=y2−3y+7y−21= y(y) + y(-3) + 7(y) + 7(-3) = y^2 - 3y + 7y - 21
Each term in the first binomial must be multiplied by each term in the second binomial.
3
Combine the like terms to simplify the expression into standard form.
Area =y2+4y−21= y^2 + 4y - 21
Combining −3y-3y and +7y+7y yields +4y+4y.

Key Concept

Finding the area of a rectangle by multiplying binomial expressions using the distributive property.
Estimated Time:45s
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Topics

Operations on Polynomials

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