Factor 16^4 y^2-250 xy^5

Name: Problem 384, Chapter 15: Algebra and Trigonometry
Uploaded: 2021-03-29T22:12:20-08:00
Duration: 23 s
Channel: Erika Bustos
Description: Factor 16^4 y^2-250 xy^5

step 1 We're given the following problem when we need to factor it. So I'm going to rewrite it as 4 fif

Question

Factor $16^{4} \mathrm{y}^{2}-250 \mathrm{xy}^{5}$

   Factor $16^{4} \mathrm{y}^{2}-250 \mathrm{xy}^{5}$

Algebra and Trigonometry

StemEZ 1st Edition

Chapter 15, Problem 384

Instant Answer

Solved by Expert Erika Bustos

03/29/2021

Step 1

So we have: 2y^2(2^12 - 5^3x^3y^3) Now, we can see that this is a difference of two cubes. Recall that the difference of cubes can be factored as (a^3 - b^3) = (a - b)(a^2 + ab + b^2). In this case, a = 2^4 and b = 5xy^3. So we have: Show more…

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Factor $16^{4} \mathrm{y}^{2}-250 \mathrm{xy}^{5}$

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Key Concepts

Greatest Common Factor (GCF)

This concept involves identifying the largest expression that divides each term of a polynomial without a remainder. By factoring out the GCF, the expression is simplified, which is often the first critical step in the factorization process.

Exponential Rules in Factoring

When an expression contains terms with exponents, it is important to apply the rules of exponents properly to determine common factors, especially when variables have different powers. This ensures that factors involving variables are correctly extracted and the remaining expression is simplified.

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