Divide and, if possible, simplify. (8 y^3-27)/(64 y^3-1) ÷(4 y^2-9)/(16 y^2+4 y+1)

Name: Problem 68, Chapter 6: Intermediate Algebra : Concepts and Applications
Uploaded: 2020-05-28T22:03:18-08:00
Duration: 2 min 19 s
Channel: Jeffrey Morris
Description: Divide and, if possible, simplify. (8 y^3-27)/(64 y^3-1) ÷(4 y^2-9)/(16 y^2+4 y+1)

step 1 All right, so I've gone ahead and factored out all of these polynomials. So in the left side, al

Divide and, if possible, simplify. (8 y^3-27)/(64 y^3-1) ÷(4...

Key Concepts

Rational Expressions

Rational expressions are fractions where the numerator and the denominator are polynomials. This concept involves performing arithmetic operations on these expressions, including division, which typically requires factoring and simplifying by canceling common factors across the numerator and denominator.

Division of Fractions

Dividing one fraction by another is accomplished by multiplying by the reciprocal of the divisor. This key concept is essential when simplifying complex rational expressions since it transforms a division problem into a multiplication problem, making it easier to factor and cancel common terms.

Factoring Polynomials

Factoring polynomials involves expressing a polynomial as a product of simpler polynomials or expressions, which can reveal common factors in the numerator and denominator. This process is crucial in simplifying rational expressions and solving equations.

Difference of Cubes

The difference of cubes is a special factoring technique where an expression of the form a^3 - b^3 is factored into (a - b)(a^2 + ab + b^2). Recognizing this pattern is important when simplifying expressions that involve cubic terms.

Difference of Squares

The difference of squares is a factoring method used for expressions of the form a^2 - b^2, which factors into (a - b)(a + b). This technique is valuable for simplifying quadratic expressions and identifying common factors in rational expressions.

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