The greatest common factor (GCF) is a term used to describe the biggest number that can divide evenly into two or more numbers. Sometimes, this is also referred to as the greatest common divisor (GCD) or highest common factor (HCF).
In this case, we have two monomials:
100x⁵y⁶ and 50x³y³
1. Separate the coefficients, and the variables.
Coefficients: 100 and 50
x - variable: x⁵ and x³
y - variable: y⁶ and y³
2. Find the GCF of the separated terms in number 1.
Coefficients: 100 and 50
In this case, 100 is divisible by 50, and 50 is divisible by itself, therefore the GCF of these two are 50.
x - variable: x⁵ and x³
In this case, x⁵ is divisible by x³ (by law of exponents, when x⁵ is divided by x³, the answer will be x²), and x³ is divisible by x³, therefore the GCF of these two are x³.
y - variable: y⁶ and y³
Same rules with x - variable, y⁶ is divisible by y³, and y³ is by itself. Therefore their GCF is y³.
Collecting and multiplying the GCF of the separared terms, the GCF of both monomials are:
Answers & Comments
Answer:
50x³y³
Step-by-step explanation:
The greatest common factor (GCF) is a term used to describe the biggest number that can divide evenly into two or more numbers. Sometimes, this is also referred to as the greatest common divisor (GCD) or highest common factor (HCF).
In this case, we have two monomials:
100x⁵y⁶ and 50x³y³
1. Separate the coefficients, and the variables.
Coefficients: 100 and 50
x - variable: x⁵ and x³
y - variable: y⁶ and y³
2. Find the GCF of the separated terms in number 1.
Coefficients: 100 and 50
In this case, 100 is divisible by 50, and 50 is divisible by itself, therefore the GCF of these two are 50.
x - variable: x⁵ and x³
In this case, x⁵ is divisible by x³ (by law of exponents, when x⁵ is divided by x³, the answer will be x²), and x³ is divisible by x³, therefore the GCF of these two are x³.
y - variable: y⁶ and y³
Same rules with x - variable, y⁶ is divisible by y³, and y³ is by itself. Therefore their GCF is y³.
Collecting and multiplying the GCF of the separared terms, the GCF of both monomials are:
50 × x³ × y³ = 50x³y³.
Answer :
(10xy³- z²)(10xy³- z²)
(10xy³- z²)(10xy³- z²)
=100x²y + 10xy³z²- 10xy ³z²
=100x²y