turn these factored equastions into expanded form:
(n-1)(n^2-3n+4)
(n^2+2)^2
Use distributive property
(n-1)(n^2-3n+4)
= n (n^2-3n+4) - 1 (n^2-3n+4)
= n^3 -3 n^2 + 4 n -n^2 + 3 n - 4
collect like terms
= n^3 -4 n^2 + 7 n - 4
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n^2 (n^2+2) + 2 (n^2+2)
= n^4 + 2 n^2 + 2 n^2 + 4
= n^4 + 4 n^2 + 4
or simply FOIL (n^2+2)(n^2+2)
use distributive property to factor each expression:1. x^2+8x+16
2. d^2+8d+7 3. y^2+6y+8 4. b^2-2b-3 5. s^2-4s-5
Grace, you are jesting. We are not going to do that for you, it will not help you learn if we do the practice. We will be happy to critique your work.
To expand the factored equations into expanded form, you need to apply the distributive property. Let's look at each of these equations separately:
1. (n-1)(n^2-3n+4)
To expand this equation, distribute the term n-1 to each term inside the parentheses:
(n-1)(n^2-3n+4) = n(n^2-3n+4) - 1(n^2-3n+4)
Now, multiply each term inside the parentheses by the term outside the parentheses:
n(n^2-3n+4) - 1(n^2-3n+4)
= n * n^2 - n * 3n + n * 4 - 1 * n^2 + 1 * 3n - 1 * 4
Simplify each term:
= n^3 - 3n^2 + 4n - n^2 + 3n - 4
= n^3 -4n^2 + 7n - 4
Therefore, the expanded form of the equation (n-1)(n^2-3n+4) is n^3 - 4n^2 + 7n - 4.
2. (n^2+2)^2
To expand this equation, you need to square the expression inside the parentheses.
(n^2+2)^2 = (n^2+2)(n^2+2)
Distribute each term inside the parentheses to each term outside the parentheses:
(n^2+2)(n^2+2) = n^2 * n^2 + n^2 * 2 + 2 * n^2 + 2 * 2
Simplify each term:
= n^4 + 2n^2 + 2n^2 + 4
= n^4 + 4n^2 + 4
Therefore, the expanded form of the equation (n^2+2)^2 is n^4 + 4n^2 + 4.