Question

11. simplify
x³(2x - 3 )+ 4x²( 3x - 1) - 6x⁵.
(2)​

Answer 1

Step-by-step explanation:

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Answer 2

First off, I notice that terms of these polynomials have some power (that is, degree) "gaps".

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The first polynomial has an x3 term, an x2 term, and a constant term, but no x term; and the second polynomial has an x3 term, an x term, and a constant term, but no x2 term. When I do the vertical multiplication, I will need to leave spaces in my set-up, corresponding to the "gaps" in the degrees of the polynomials' terms, because I will almost certainly need the space.

(This is similar to using zeroes as "place holders" in regular numbers. You might have a thousands digit of 3, a hundreds digit of 2, and a units digit of 5, so you'd put a 0 in for the tens digits, creating the number 3,205.)

Here's what that looks like:

x^3 + 2x^2 + 4 is over 2x^3 + x + 1; first row: +1 * +4 = +4, to below +1; +1 * +2x^2 = +2x^2, two spaces to left of +4; +1 * x^3 = +x^3, to left of +2x^2; second row: +x * +4 = +4x, to below x in 2nd poly; +x * 2x^2 = +2x^3, to below +x^3; +x * x^3 = x^4, to left of +2x^3; third row: 2x^3 * +4 = +8x^3, to below +2x^3; 2x^3 * +2x^2 = +4x^5, two spaces to left of +8x^3; 2x^3 * x^3 = 2x^6, to left of +4x^5; adding down: 2x^3 + 4x^5 + x^4 + x^3 + 2x^3 + 8x^3 + 2x^2 + 4x + 4 = 2x^6 + 4x^5 + x^4 + 11x^3 + 2x^2 + 4x + 4