$8 x^2 y^2+4 x^2-12 x$
Answer (1)
Identify the greatest common factor (GCF) of the terms in the expression.
Factor out the GCF from the expression.
The factored form of the expression 8 x 2 y 2 + 4 x 2 − 12 x is 4 x ( 2 x y 2 + x − 3 ) .
Explanation
Understanding the Problem We are given the expression 8 x 2 y 2 + 4 x 2 − 12 x and asked to analyze it. Our goal is to factor the expression.
Finding the Greatest Common Factor First, we identify the greatest common factor (GCF) of the terms 8 x 2 y 2 , 4 x 2 , and − 12 x . The GCF of the coefficients 8, 4, and -12 is 4. The GCF of the variable terms x 2 y 2 , x 2 , and x is x . Therefore, the GCF of the entire expression is 4 x .
Factoring out the GCF Next, we factor out the GCF, 4 x , from each term in the expression:
8 x 2 y 2 + 4 x 2 − 12 x = 4 x ( 2 x y 2 + x − 3 )
Final Answer The factored form of the expression 8 x 2 y 2 + 4 x 2 − 12 x is 4 x ( 2 x y 2 + x − 3 ) .
Examples
Factoring expressions is a fundamental skill in algebra and is used in many real-world applications. For example, engineers use factoring to simplify equations when designing structures or analyzing circuits. Similarly, economists use factoring to model and predict economic trends. Factoring helps to break down complex problems into simpler, more manageable parts, making it easier to find solutions and make informed decisions.
