Multiply the binomial and trinomial (x-2)(x^2+2x+4)
Can someone please help ? I do not understand what to do.
Thank You
x^3-8
Sure, I can help! To multiply the binomial (x - 2) and the trinomial (x^2 + 2x + 4), you use the distributive property. This means that you'll multiply each term in the binomial by each term in the trinomial, and then combine like terms.
Let's break it down step by step.
First, let's multiply the first term of the binomial (x) by each term in the trinomial:
x * x^2 = x^3
x * 2x = 2x^2
x * 4 = 4x
Next, let's multiply the second term of the binomial (-2) by each term in the trinomial:
-2 * x^2 = -2x^2
-2 * 2x = -4x
-2 * 4 = -8
Now, we can combine all the like terms:
x^3 + 2x^2 - 2x^2 + 4x - 4x - 8
Simplifying further:
x^3 + 4x - 8
So, when you multiply (x - 2)(x^2 + 2x + 4), you get x^3 + 4x - 8.
I hope that clears things up! Let me know if you have any other questions.
To multiply the binomial (x - 2) by the trinomial (x^2 + 2x + 4), you can use the distributive property.
Step 1: Multiply the first term of the binomial by each term of the trinomial:
(x)(x^2) = x^3
(x)(2x) = 2x^2
(x)(4) = 4x
Step 2: Multiply the second term of the binomial by each term of the trinomial:
(-2)(x^2) = -2x^2
(-2)(2x) = -4x
(-2)(4) = -8
Step 3: Combine the like terms:
x^3 + 2x^2 + 4x - 2x^2 - 4x - 8
Step 4: Simplify the expression:
The x^2 terms (-2x^2 and 2x^2) cancel each other out, and the x terms (4x and -4x) cancel each other out as well. So, the simplified expression becomes:
x^3 - 8
Therefore, the product of (x - 2) and (x^2 + 2x + 4) is x^3 - 8.
Of course, I can help you with that!
To multiply a binomial and a trinomial, you will need to use the distributive property. The distributive property states that when multiplying a term by a sum or difference, you need to multiply the term by each term in the sum or difference, and then sum up the results.
Let's break it down step by step:
1. Multiply the first term of the binomial (x) by each term in the trinomial (x^2, 2x, and 4).
So, you get:
x * x^2 = x^3
x * 2x = 2x^2
x * 4 = 4x
2. Next, multiply the second term of the binomial (-2) by each term in the trinomial.
So, you get:
-2 * x^2 = -2x^2
-2 * 2x = -4x
-2 * 4 = -8
3. Finally, add up all the terms that you obtained in the previous steps.
Combining like terms, you get:
x^3 + 2x^2 + 4x - 2x^2 - 4x - 8
The terms 2x^2 and 4x occur twice, but with opposite signs, so they cancel each other out.
Simplifying further, you get:
x^3 - 8
Therefore, the product of (x-2)(x^2+2x+4) is x^3 - 8.
I hope this explanation helps! Let me know if you have any further questions.