simplify (x+3)(x^4-4x^2+5) Can you tell me the steps to take? I think I need to reorder it, but I don't know how.
Yes you do need to reorder it. I looks confusing right now
Just use the distributive property:
(x+3)(x^4-4x^2+5)
= (x+3)(x^4) + (x+3)(-4x^2) + (x+3)(5)
= x^5 + 3x^4 - 4x^3 - 12x^2 + 5x + 15
To simplify the expression (x+3)(x^4-4x^2+5), you need to use the Distributive Property. This property states that when you multiply a term outside parentheses by each term inside the parentheses, you will get a new expression.
Let's break down the steps to simplify the expression:
1. First, distribute the x term to each term inside the parentheses:
(x)(x^4) + (x)(-4x^2) + (x)(5)
This gives you: x^5 - 4x^3 + 5x
2. Next, distribute the 3 term to each term inside the parentheses:
(3)(x^4) + (3)(-4x^2) + (3)(5)
This gives you: 3x^4 - 12x^2 + 15
3. Now, combine all the terms you obtained in steps 1 and 2:
(x+3)(x^4-4x^2+5) = (x^5 - 4x^3 + 5x) + (3x^4 - 12x^2 + 15)
4. Finally, combine like terms if possible:
(x^5 + 3x^4) + (- 4x^3 - 12x^2 + 5x + 15)
This is the simplified form of the expression (x+3)(x^4-4x^2+5).