Multiplying Polynomials (Box Method)

Front

What is the Box Method used for in mathematics?

Back

The Box Method is a visual technique used to multiply polynomials by organizing the terms into a box or grid format, allowing for easier calculation of products.

Front

How do you set up the Box Method for multiplying (x + 3)(2x - 4)?

Back

You create a box with two rows and two columns, placing (x + 3) on one side and (2x - 4) on the other, then fill in the boxes with the products of the terms.

Front

What is the result of multiplying 5x by (-3x + 5) using the distributive property?

Back

The result is -15x² + 25x.

Front

Define like terms in algebra.

Back

Like terms are terms that have the same variable raised to the same power, allowing them to be combined through addition or subtraction.

Front

Give an example of like terms.

Back

y² and 2y² are like terms because they both contain the variable y raised to the same power.

Front

What is the product of x² and x³?

Back

The product is x⁵, obtained by adding the exponents (2 + 3 = 5).

Front

What is the expanded form of the product (x + 3)(x + 6)?

Back

The expanded form is x² + 9x + 18.

Front

What is the first step in multiplying two binomials using the Box Method?

Back

The first step is to set up a box or grid with one binomial along the top and the other along the side.

Front

How do you combine like terms after using the Box Method?

Back

After filling in the box with products, you combine the coefficients of like terms to simplify the expression.

Front

What is the significance of the coefficients in polynomial multiplication?

Back

Coefficients are the numerical factors in terms of a polynomial, and they determine the magnitude of each term in the final product.