1. Find the GCF of the following:
a) xy, y2x, x2y
b) x2, x3, x3
c) y2(2y - 1), 3(2y - 1)
how do i do this can someone please explain'
which factor is found in all of your terms?
e.g. xy, y2x, x2y
I see xy in the first, the 2nd and the 3rd term, so xy is the HCF
You appear to have a typo in the 2nd question
x^3 appears twice, unless that was the intention.
Y2x
To find the Greatest Common Factor (GCF) of the given expressions, follow these steps:
a) Find the GCF of xy, y2x, x2y:
Step 1: Write each term in its factored form, if possible.
xy = x * y
y2x = y * y * x
x2y = x * x * y
Step 2: Identify the common factors in each term.
The common factors are x and y.
Step 3: Determine the lowest exponent for each common factor.
The lowest exponent for x is 1, and for y is 1.
Step 4: Multiply the common factors with their lowest exponents.
GCF = x^1 * y^1
GCF = xy
Therefore, the GCF of xy, y2x, x2y is xy.
b) Find the GCF of x2, x3, x3:
Step 1: Write each term in its factored form, if possible.
x2 = x * x
x3 = x * x * x
x3 = x * x * x
Step 2: Identify the common factors in each term.
The common factor is x.
Step 3: Determine the lowest exponent for the common factor.
The lowest exponent for x is 1.
Step 4: Multiply the common factor with its lowest exponent.
GCF = x^1
GCF = x
Therefore, the GCF of x2, x3, x3 is x.
c) Find the GCF of y2(2y - 1), 3(2y - 1):
Step 1: Observe that the expression (2y - 1) is common to both terms.
Step 2: Identify the common factor (2y - 1).
Step 3: Since the expression (2y - 1) cannot be simplified further, it becomes the GCF.
Therefore, the GCF of y2(2y - 1), 3(2y - 1) is 2y - 1.
To find the Greatest Common Factor (GCF), follow these steps:
Step 1: Write each term in its prime factorization form.
Step 2: Identify the common factors.
Step 3: Multiply the common factors together to find the GCF.
Now, let's apply these steps to solve the given problems:
a) For the terms xy, y2x, x2y:
1. The prime factorization of xy is x * y.
2. The prime factorization of y2x can be rearranged as y * y * x.
3. The prime factorization of x2y can be rearranged as x * x * y.
4. Looking at the prime factorizations, you can observe that the common factors are x and y.
5. Multiply x and y together to get the GCF of xy, y2x, x2y.
GCF = x * y = xy
b) For the terms x2, x3, x3:
1. The prime factorization of x2 is x * x.
2. The prime factorization of x3 can be rearranged as x * x * x.
3. The prime factorization of x3 can also be written as x2 * x.
4. Looking at the prime factorizations, you can observe that the common factor is x * x (x squared).
5. Therefore, the GCF of x2, x3, x3 is x2.
c) For the terms y2(2y - 1) and 3(2y - 1):
1. Expand y2(2y - 1) to get 2y3 - y2.
2. Multiply 3 by (2y - 1) to get 6y - 3.
3. The prime factorization of 2y3 - y2 can be rearranged as y2 * y * 2 - y2.
4. The prime factorization of 6y - 3 can be rearranged as 3 * 2 * (2y - 1).
5. Notice that (2y - 1) is a common factor.
6. Multiply (2y - 1) with the remaining factors to get the GCF of y2(2y - 1) and 3(2y - 1).
GCF = (2y - 1) * y2
= 2y3 - y2.
By following these steps, you can find the GCF for different sets of terms.