Perform each division. See Examples 7 and 8. $$(8wxy2+3wx2y+12w2xy)/(4wx2y)(8wxy^2+3wx^2$y+12w^2$xy)/(4wx^2y)$$

Ch. R - Review of Basic Concepts

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Lial 13th Edition

Ch. R - Review of Basic Concepts

문제 87

1장, 문제 87

Perform each division. See Examples 7 and 8. $(8 w x y^{2} + 3 w x^{2} y + 12 w^{2} x y) / (4 w x^{2} y)$

검증된 단계별 안내

Identify the division problem: $\frac{8wxy^{2} + 3wx^{2}y + 12w^{2}xy}{4wx^{2}y}$.

Rewrite the expression as the sum of three separate fractions: $\frac{8wxy^{2}}{4wx^{2}y} + \frac{3wx^{2}y}{4wx^{2}y} + \frac{12w^{2}xy}{4wx^{2}y}$.

Simplify each fraction individually by canceling common factors in the numerator and denominator:

- For $\frac{8wxy^{2}}{4wx^{2}y}$, cancel common variables and coefficients.

- For $\frac{3wx^{2}y}{4wx^{2}y}$, cancel common variables and coefficients.

- For $\frac{12w^{2}xy}{4wx^{2}y}$, cancel common variables and coefficients.

After simplifying each term, combine the results to write the final simplified expression.

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영상 길이:

주요 개념

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

Polynomial Division

Polynomial division involves dividing one polynomial by another, similar to numerical division. Each term in the numerator is divided by the denominator, simplifying the expression step-by-step. Understanding how to divide terms with variables and exponents is essential.

Laws of Exponents

The laws of exponents govern how to handle powers when multiplying, dividing, or raising powers to powers. For division, subtract the exponents of like bases. This is crucial when simplifying terms like w^a / w^b or x^a / x^b in the expression.

Combining Like Terms

After dividing each term, combining like terms means adding or subtracting terms with the same variables raised to the same powers. This step simplifies the expression to its simplest form, making it easier to interpret or use in further calculations.

Perform each division. See Examples 7 and 8. (8wxy2+3wx2y+12w2xy)/(4wx2y)(8wxy^2+3wx^2y+12w^2xy)/(4wx^2y)