Use the table below to find the products of the two polynomials. Enter your answer in descending order in the box below. Enter exponents using the caret ( ^ ). For example, you would enter as 4x^2. Do not enter spaces in your answer.
(x3 + 2x2 - 2)(x3 - 3x + 3)how do you do this?
it was wrong the first one
Just multiply term by term, just as you do with a multi-digit number:
124* 327 = 100(300+20+7) + 20(300+20+7) + 4(300+20+7)
(x^3 + 2x^2 - 2)(x^3 - 3x + 3)
= x^3(x^3 - 3x + 3) + 2x^2(x^3 - 3x + 3) - 2(x^3 - 3x + 3)
= x^6 - 3x^4 + 3x^3 + 2x^5 - 6x^3 + 6x^2 - 2x^3 + 6x - 6
= x^6 + 2x^5 - 3x^4 - 5x^3 + 6x^2 + 12x - 6
Ahem. Make that + 6x
thanks :)
(x7 + x4 + x)(x3 - 1)
can u help me with this one 2
To find the products of the two polynomials, we can use the distributive property of multiplication.
First, let's break down the given expression:
(x^3 + 2x^2 - 2)(x^3 - 3x + 3)
To simplify this, we need to multiply each term in the first polynomial by each term in the second polynomial.
Let's start by multiplying the first term of the first polynomial (x^3) by each term of the second polynomial:
(x^3)(x^3) = x^(3+3) = x^6
(x^3)(-3x) = -3x^(3+1) = -3x^4
(x^3)(3) = 3x^3
Next, we multiply the second term of the first polynomial (2x^2) with each term of the second polynomial:
(2x^2)(x^3) = 2x^(2+3) = 2x^5
(2x^2)(-3x) = -6x^(2+1) = -6x^3
(2x^2)(3) = 6x^2
Finally, we multiply the last term of the first polynomial (-2) with each term of the second polynomial:
(-2)(x^3) = -2x^3
(-2)(-3x) = 6x
(-2)(3) = -6
Now, we can combine all the products we obtained:
x^6 + (-3x^4) + 3x^3 + 2x^5 + (-6x^3) + 6x^2 + (-2x^3) + 6x + (-6)
Simplifying further, we can combine like terms:
x^6 + 2x^5 - 3x^4 + 3x^3 - 8x^3 + 6x^2 + 6x - 6
Therefore, the expression (x^3 + 2x^2 - 2)(x^3 - 3x + 3) simplifies to:
x^6 + 2x^5 - 3x^4 - 2x^3 + 6x^2 + 6x - 6