Factor by any method. See Examples 1–7. $$1000x3+343y31000x^3$+343y^3$$

Ch. R - Review of Basic Concepts

Lial13th EditionCollege AlgebraISBN: 9780136881063당신이 사용하는 게 아니라요?교과서 변경

모든 교과서

Lial 13th Edition

Ch. R - Review of Basic Concepts

문제 103

1장, 문제 103

Factor by any method. See Examples 1–7. $1000 x cubed plus 343 y cubed$

검증된 단계별 안내

Recognize that the expression $1000x^3 + 343y^3$ is a sum of cubes because $1000x^3 = (10x)^3$ and $343y^3 = (7y)^3$.

Recall the sum of cubes factoring formula: $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$.

Identify $a = 10x$ and $b = 7y$ in the given expression.

Apply the formula by substituting $a$ and $b$: write the factorization as $(10x + 7y)((10x)^2 - (10x)(7y) + (7y)^2)$.

Simplify the terms inside the second factor: calculate $(10x)^2$, $(10x)(7y)$, and $(7y)^2$ to complete the factorization.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Sum of Cubes Formula

The sum of cubes formula states that a³ + b³ = (a + b)(a² - ab + b²). This formula is used to factor expressions where two terms are each perfect cubes added together. Recognizing 1000x³ and 343y³ as cubes allows applying this formula directly.

Identifying Perfect Cubes

A perfect cube is a number or expression raised to the third power, such as 1000 = 10³ and 343 = 7³. Identifying each term as a perfect cube is essential before applying the sum of cubes formula, ensuring the expression fits the pattern a³ + b³.

Factoring Polynomials

Factoring polynomials involves rewriting an expression as a product of simpler polynomials. Using special formulas like the sum of cubes helps break down complex expressions into factors, which can simplify solving equations or further algebraic manipulation.

Factor by any method. See Examples 1–7. 1000x3+343y31000x^3+343y^3