how do I rewrite the following expression as an equivalent product of two binomials?
x(x+2)+3(x+2)
Factor out the common x + 2
(x+2)(x+3)
Once you factor out(x+2) what is left is just x +3
To rewrite the expression x(x+2)+3(x+2) as an equivalent product of two binomials, you can use the distributive property.
Step 1: First, let's rewrite the expression without the parentheses:
x(x+2) + 3(x+2)
Step 2: Now, using the distributive property, we multiply each term in the parentheses by the corresponding terms outside the parentheses:
(x * x) + (x * 2) + (3 * x) + (3 * 2)
Step 3: Simplify each term:
x^2 + 2x + 3x + 6
Step 4: Combine like terms:
x^2 + 5x + 6
Therefore, the equivalent product of two binomials is:
(x + 2)(x + 3)
To rewrite the given expression as an equivalent product of two binomials, follow these steps:
Step 1: Identify common factors.
In the given expression, the binomial (x + 2) appears in both terms. We can factor out this common binomial as follows:
x(x + 2) + 3(x + 2)
Step 2: Factor out the common binomial.
Factor out (x + 2) from both terms:
(x + 2)(x) + (x + 2)(3)
Step 3: Simplify the expression.
Now, we have a common binomial, (x + 2), which can be factored out. Simplify the expression by multiplying the common binomial with the remaining terms:
(x + 2)(x) + (x + 2)(3)
= x(x + 2) + 3(x + 2)
= x * x + x * 2 + 3 * x + 3 * 2
Perform the multiplication:
= x^2 + 2x + 3x + 6
Now, combine like terms:
= x^2 + 5x + 6
Thus, the original expression x(x+2) + 3(x+2) can be rewritten as an equivalent product of two binomials: (x + 2)(x + 3).