Using multiplication properties calculate (a-2b)(a^2+4b^2)(a+2b)
- print Print
- list Cite
Expert Answers
calendarEducator since 2010
write12,544 answers
starTop subjects are Math, Science, and Business
We need to simplify: (a-2b)(a^2+4b^2)(a+2b)
Use (a - b)(a +b) = a^2 - b^2
(a-2b)(a^2+4b^2)(a+2b)
=> (a-2b)(a+2b)(a^2+4b^2)
=> (a^2 - 4b^2)(a^2+4b^2)
=> a^4 - 16b^4
The required result is a^4 - 16b^4
Related Questions
- Calculate sqrt(7225) without using a calculator.
- 1 Educator Answer
- Using properties of determinant prove that `|[1, a, a^2],[1, b, b^2],[1, c, c^2]| = (a-b)(b-c)(c-a)`
- 1 Educator Answer
- `arcsec(-sqrt(2))` Evaluate the expression without using a calculator
- 1 Educator Answer
- Calculate the multiplicative inverse of (3+4i)/(4-5i).
- 1 Educator Answer
- Use contraposition to prove that if n^2 is a multiple of 3, then n is a multiple of 3.Please show...
- 1 Educator Answer
First, we'll apply the commutative property for the 2nd and 3rd factors:
(a^2+4b^2)(a+2b) = (a+2b)(a^2+4b^2)
We'll re-write the product:
(a-2b)(a+2b)(a^2+4b^2)
We notice that the product of the first 2 factors could be replaced by the difference of squares:
(a^2 - 4b^2)(a^2+4b^2)
This product could be also replaced by its equivalent difference of squares:
(a^2 - 4b^2)(a^2+4b^2) = (a^2)^2 - (4b^2)^2
(a^2 - 4b^2)(a^2+4b^2) = a^4 - 16b^4
The result of the product is: (a-2b)(a^2+4b^2)(a+2b)=a^4 - 16b^4
Unlock This Answer Now
Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.
Student Answers