Studdy AI Logo
Math

Question Simplify the expression (r+f+6)(r+f−6)(r+f+6)(r+f-6).

Studdy Solution

STEP 1

Assumptions
1. We are given an expression in the form (a+b)(a−b)(a+b)(a-b).
2. We need to simplify the expression.
3. The expression (a+b)(a−b)(a+b)(a-b) is recognized as a difference of squares, which can be simplified to a2−b2a^2 - b^2.

STEP 2

Identify the terms aa and bb in the given expression (r+f+6)(r+f−6)(r+f+6)(r+f-6).
a=r+fa = r+f b=6b = 6

STEP 3

Apply the difference of squares formula to the given expression.
(a+b)(a−b)=a2−b2 (a+b)(a-b) = a^2 - b^2

STEP 4

Substitute a=r+fa = r+f and b=6b = 6 into the difference of squares formula.
(r+f+6)(r+f−6)=(r+f)2−62 (r+f+6)(r+f-6) = (r+f)^2 - 6^2

STEP 5

Expand the square of the binomial (r+f)2(r+f)^2.
(r+f)2=r2+2rf+f2 (r+f)^2 = r^2 + 2rf + f^2

STEP 6

Calculate the square of bb, which is 626^2.
62=36 6^2 = 36

STEP 7

Substitute the expanded binomial and the value of 626^2 back into the difference of squares formula.
(r+f+6)(r+f−6)=r2+2rf+f2−36 (r+f+6)(r+f-6) = r^2 + 2rf + f^2 - 36

STEP 8

Write the simplified expression.
(r+f+6)(r+f−6)=r2+2rf+f2−36 (r+f+6)(r+f-6) = r^2 + 2rf + f^2 - 36
The simplified expression is r2+2rf+f2−36r^2 + 2rf + f^2 - 36.

Was this helpful?

Studdy solves anything!

banner

Start learning now

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

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord