In most of the previous examples there were only two terms. Extend your work with using the distributive law backwards and write the following as a product of binomials. x(x+2)+3(x+2)+4x(x+2)
factor out the common (x+2) and you have
x(x+2)+3(x+2)+4x(x+2)
= (x+3+4x)(x+2)
...
Sure thing! Let's distribute the terms using the distributive law:
x(x+2) + 3(x+2) + 4x(x+2)
First, let's distribute the x to the terms inside the parentheses:
x^2 + 2x + 3(x+2) + 4x(x+2)
Next, let's distribute the 3 to the terms inside the parentheses:
x^2 + 2x + 3x + 6 + 4x(x+2)
Now, let's distribute the 4x to the terms inside the parentheses:
x^2 + 2x + 3x + 6 + 4x^2 + 8x
Combining like terms, we get:
5x^2 + 13x + 6
So, the expression x(x+2) + 3(x+2) + 4x(x+2) can be written as the product of binomials:
(5x+2)(x+3)
Hope that brings a smile to your face! If you have any more questions, feel free to ask!
To write the expression x(x+2)+3(x+2)+4x(x+2) as a product of binomials, we can use the distributive property in reverse.
Step 1: Group the terms that have the same factors.
x(x+2) + 3(x+2) + 4x(x+2)
Step 2: Identify the common factor in each group.
In this case, (x+2) is the common factor in each group.
Step 3: Write the expression using the common factor.
(x+2)(x) + (x+2)(3) + (x+2)(4x)
Step 4: Simplify each term using FOIL (First, Outer, Inner, Last).
(x^2 + 2x) + (3x + 6) + (4x^2 + 8x)
Step 5: Combine like terms if possible.
x^2 + 2x + 3x + 6 + 4x^2 + 8x
Step 6: Rearrange the terms in ascending order of exponents.
4x^2 + x^2 + 2x + 3x + 8x + 6
Step 7: Combine like terms again.
5x^2 + 13x + 6
Therefore, the expression x(x+2)+3(x+2)+4x(x+2) can be written as a product of binomials as (x+2)(5x^2 + 13x + 6).
To write the expression \(x(x+2)+3(x+2)+4x(x+2)\) as a product of binomials, we can use the distributive law backwards.
Let's start by factoring out the common binomial factor \((x+2)\) from each term of the expression:
\(x(x+2)+3(x+2)+4x(x+2)\)
Using the distributive property, we can write the expression as:
\((x+2)(x) + (x+2)(3) + (x+2)(4x)\)
Applying the distributive property again, we can simplify further:
\(x^2+2x + 3x+6 + 4x^2 + 8x\)
Now, combine like terms:
\(x^2 + 4x^2 + 2x + 3x + 8x + 6\)
Combine the like terms and simplify:
\(5x^2 + 13x + 6\)
So, the expression \(x(x+2)+3(x+2)+4x(x+2)\) can be written as the product of binomials:
\((x+2)(5x+3)\)