The Product of 6x-y and 2x-y+2
What is the Product of 6x-y and 2x-y+2?
When we are given two algebraic expressions, we need to find their product. The product of two expressions is obtained by multiplying them together. In this article, we will find the product of 6x-y and 2x-y+2.
Step 1: Distributive Property
To find the product of 6x-y and 2x-y+2, we can use the distributive property. The distributive property states that we can multiply a single term by each term in the other expression.
Distributive Property Formula:
a(x + b) = ax + ab
Applying the Distributive Property
We can apply the distributive property to the given expressions as follows:
(6x-y)(2x-y+2)
= 6x(2x-y+2) – y(2x-y+2)
Step 2: Multiply the Terms
Now, we can multiply the terms in the expressions.
Multiplying the Terms:
6x(2x-y+2) = 12x^2 – 6xy + 12x
y(2x-y+2) = 2xy – y^2 – 2y
Step 3: Combine Like Terms
Now, we can combine like terms in the expressions.
Combining Like Terms:
12x^2 – 6xy + 12x – 2xy + y^2 + 2y
= 12x^2 – 8xy + y^2 + 2y
Step 4: Factor the Expression (if possible)
We can try to factor the expression, if possible.
Factoring the Expression:
12x^2 – 8xy + y^2 + 2y
= (3x – y)(4x + y)
Step 5: Simplify the Expression
We can simplify the expression by combining like terms.
Simplifying the Expression:
(3x – y)(4x + y)
= 12x^2 + 3xy – 4xy – y^2
= 12x^2 – xy – y^2
The Product of 6x-y and 2x-y+2
The product of 6x-y and 2x-y+2 is 12x^2 – xy – y^2.
Important Points:
- The distributive property is used to multiply the terms in the expressions.
- Like terms are combined to simplify the expression.
- The expression can be factored if possible.
- The product of 6x-y and 2x-y+2 is 12x^2 – xy – y^2.
Conclusion:
In this article, we have found the product of 6x-y and 2x-y+2. The product is 12x^2 – xy – y^2. This expression can be factored if possible, and it can be simplified by combining like terms. The distributive property is used to multiply the terms in the expressions, and like terms are combined to simplify the expression.