QuestionFind the product of $(5d + 4)(5d - 4)$ and simplify it.

Studdy Solution

STEP 1

Assumptions1. We are asked to find the product of two binomials $(5d+4)$ and $(5d-4)$ . . We will use the distributive property (also known as the FOIL method) to expand the product.

STEP 2

The FOIL method stands for First, Outer, Inner, Last. It is a method for multiplying two binomials. Let's apply it to our problem.
First, multiply the first terms in each binomial $First = (5d) \times (5d)$

STEP 3

Now, calculate the product of the first terms.
$First = (5d) \times (5d) =25d^{2}$

STEP 4

Next, multiply the outer terms in each binomial $Outer = (d) \times (-4)$

STEP 5

Now, calculate the product of the outer terms.
$Outer = (5d) \times (-4) = -20d$

STEP 6

Next, multiply the inner terms in each binomial $Inner = (4) \times (5d)$

STEP 7

Now, calculate the product of the inner terms.
$Inner = (4) \times (5d) =20d$

STEP 8

Finally, multiply the last terms in each binomial $Last = (4) \times (-4)$

STEP 9

Now, calculate the product of the last terms.
$Last = (4) \times (-4) = -16$

STEP 10

Now that we have the products of the first, outer, inner, and last terms, we can add them together to find the product of the two binomials.
$Product = First + Outer + Inner + Last$

STEP 11

Plug in the values for the first, outer, inner, and last terms to calculate the product.
$Product =25d^{} -20d +20d -16$

STEP 12

implify the product by combining like terms.
$Product =25d^{2} -16$ So, the product of $(5d+4)$ and $(5d-4)$ is $25d^{2} -16$ .

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms