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Question

Difficulty: EasyMultiplying Polynomials

Calculate the product of the binomials (m−6)(m - 6) and (m+2)(m + 2). What is the resulting polynomial in simplest form?

  1. m2−4m−12m^2 - 4m - 12Answer
  2. B
    m2−12m^2 - 12
  3. C
    m2+4m−12m^2 + 4m - 12
  4. D
    m2−4m+12m^2 - 4m + 12

Answer

The correct answer is the polynomial m2−4m−12m^2 - 4m - 12.
The correct answer is obtained by distributing each term in the first binomial to each term in the second binomial, which gives m2+2m−6m−12m^2 + 2m - 6m - 12. Combining the like terms (2m−6m2m - 6m) yields −4m-4m, resulting in the final simplified polynomial m2−4m−12m^2 - 4m - 12.

Step-by-Step Solution

1
Apply the distributive property to multiply each term in the first binomial by each term in the second binomial.
m⋅m+m⋅2−6⋅m−6⋅2m \cdot m + m \cdot 2 - 6 \cdot m - 6 \cdot 2
To expand the product of the two binomial expressions.
2
Perform the individual multiplications for each term.
m2+2m−6m−12m^2 + 2m - 6m - 12
To simplify the expression before combining any like terms.
3
Combine the like terms (the middle terms containing mm).
m2−4m−12m^2 - 4m - 12
To write the polynomial in its standard, fully simplified form.

Key Concept

Multiplying Polynomials

Alternative Method

You can use the area model (or box method) to organize the multiplication. Draw a 2x2 grid, place the terms mm and −6-6 along the top edge, and mm and 22 along the side. Multiply the intersecting terms to fill the four cells (m2m^2, −6m-6m, 2m2m, and −12-12), and then sum all the cells to find the final polynomial.
Estimated Time:45s
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Topics

Multiplying Polynomials

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