Question

Factorize: x^2/y^2-a^2/b^2

A. Apply the rules of factorization tox^2/y^2-a^2/b^2
B. Utilize the correct steps for factoring rational expressions.
C. Understand the rules governing the factorization of the given expression.
D. Apply the principles of algebra to factorize the expression.
Rules for Factorizing
A. Factorizing trinomials involves breaking them into product of two binomials.
B. The rules for factorizing include finding common factors and using the distributive property.
C. Factoring requires identifying patterns and applying corresponding methods.
D. The factorization of trinomials follows a systematic approach.
How to Factorize Trinomials
A. Trinomials can be factorized by finding two binomials whose product results in the original expression.
B. Factoring involves identifying factors that multiply to yield the trinomial.
C. The process of factorization for trinomials includes factoring out the greatest common factor.
D. Factorizing trinomials is a methodical process involving trial and error.

Answer 1

To factorize the expression x^2/y^2 - a^2/b^2, it is recognized as a difference of squares and factored into the product (x/y + a/b)(x/y - a/b).

Step-by-step explanation:

Factorizing the Given Expression

To factorize the expression x^2/y^2 - a^2/b^2, we will apply the rules of algebra and look for patterns that can simplify the expression into a factored form. The given expression resembles the difference of squares pattern, which is expressed as A^2 - B^2 = (A + B)(A - B). In this case, our A is x/y and B is a/b. Applying the difference of squares to our expression, we get:

(x/y)^2 - (a/b)^2 = (x/y + a/b)(x/y - a/b)

The expression is now factorized into the product of two binomials.a