Question

Find the product of (−x+2)(x−7) by using the horizontal method.

What will you multiply by (−x+2) to find the first product?
What will you multiply by (−x+2) to find the second product?
What is the product of (−x+2)(x−7) written in standard form?

Answer 1

The product of the binomials (-x+2) and (x-7) is found using the horizontal method to generate four products and then combining like terms to get the final result in standard form: -x² + 9x - 14.

Step-by-step explanation:

To find the product of two binomials, such as (-x+2)(x-7), we use the distributive property, sometimes known as the FOIL method when dealing with binomials. However, when using the horizontal method, each term in the first binomial is multiplied by each term in the second binomial.

The first product is found by multiplying the -x from the first binomial by the x from the second binomial:

• -x × x = -x²

The second product is found by multiplying the -x from the first binomial by the -7 from the second binomial:

• -x × (-7) = +7x due to the rule that the product of two negative numbers yields a positive result.

The third product is found by multiplying the 2 from the first binomial by the x from the second binomial:

• 2 × x = 2x

Lastly, the fourth product is the multiplication of 2 from the first binomial by -7 from the second binomial:

• 2 × (-7) = -14 due to the rule that the product of numbers with opposite signs yields a negative result.

Combining all these, the product in standard form is:

-x² + 7x + 2x - 14

Simplifying by combining like terms:

-x² + 9x - 14