a) 2ax-6bx+ay-3by
b) 2ax-6bx-ay+3by
c) a^2b+c^2b-c^2b-a^2b
d) a^3+3a^2+2a+6
e) ax-2ay+2bx-4by
skill comes from experience. Just look for common factors.
2ax-6bx+ay-3by
You have a 2and a 6, and a 1 and a 3. So,
2x(a-3b)+y(a-3b)
(2x+y)(a-3b)
Now you try the others.
a) To simplify the expression 2ax-6bx+ay-3by, you can combine like terms. Like terms have the same variables raised to the same power. First, let's look at the terms that have 'a' as a variable: 2ax and ay. Since both terms have the variable 'a' raised to the power of 1, we can combine them by adding their coefficients (numbers in front of the variable).
So, 2ax + ay = (2a + 1) * x
Now let's look at the terms that have 'b' as a variable: -6bx and -3by. Again, both terms have the variable 'b' raised to the power of 1, so we can combine them by adding their coefficients.
So, -6bx - 3by = (-6b - 3b) * x
Therefore, the simplified expression is: (2a + 1) * x + (-6b - 3b) * x
b) Similar to the previous expression, to simplify 2ax-6bx-ay+3by, we combine like terms.
The terms with 'a' as a variable are 2ax and -ay. Since both terms have 'a' raised to the power of 1, we can combine them by adding their coefficients:
So, 2ax - ay = (2a - 1) * x
The terms with 'b' as a variable are -6bx and 3by. Since both terms have 'b' raised to the power of 1, we can combine them by adding their coefficients:
So, -6bx + 3by = (-6b + 3b) * x
Therefore, the simplified expression is: (2a - 1) * x + (-6b + 3b) * x
c) In the expression a^2b + c^2b - c^2b - a^2b, we can simplify it by combining like terms.
The terms with 'a^2b' and '-a^2b' have the same variables and powers; therefore, we can subtract them:
So, a^2b - a^2b = 0
The terms with 'c^2b' and '-c^2b' also have the same variables and powers; subtracting them gives:
So, c^2b - c^2b = 0
Hence, after simplifying, we are left with 0.
d) The expression a^3 + 3a^2 + 2a + 6 does not have any like terms to combine, so it is already in its simplified form.
e) To simplify the expression ax - 2ay + 2bx - 4by, we can combine like terms. The terms with 'a' as a variable are ax and 2ax. Since both terms have 'a' raised to the power of 1, we can combine them by adding their coefficients:
So, ax + 2ax = (1 + 2) * x
The terms with 'b' as a variable are -2ay and -4by. We can combine them by adding their coefficients:
So, -2ay - 4by = (-2a - 4a) * y
Therefore, the simplified expression is: 3ax + (-6b - 4a) * y.