Ask Question
2 November, 05:37

Multiply 3x^2 (5x^3)

+2
Answers (2)
  1. 2 November, 07:03
    0
    15x^5

    Step-by-step explanation:

    Multiply the integers and add the powers.

    That's

    3 x 5 x^2+3

    15x^5
  2. 2 November, 07:27
    0
    Step-by-step explanation:

    Here's what the multiplication looks like when it's done horizontally:

    (4x2 - 4x - 7) (x + 3)

    (4x2 - 4x - 7) (x) + (4x2 - 4x - 7) (3)

    4x2 (x) - 4x (x) - 7 (x) + 4x2 (3) - 4x (3) - 7 (3)

    4x3 - 4x2 - 7x + 12x2 - 12x - 21

    4x3 - 4x2 + 12x2 - 7x - 12x - 21

    4x3 + 8x2 - 19x - 21

    That was painful! Now I'll do it vertically:

    4x^2 - 4x - 7 is positioned above x + 3; first row: + 3 times - 7 is - 21, carried down below the + 3; + 3 times - 4x is - 12x, carried down below the x; + 3 times 4x^2 is + 12x^2, carried down to the left of the - 12x; second row: x times - 7 is - 7x, carried down below the - 12x; x times - 4x is - 4x^2, carried down below the + 12x^2; x times 4x^2 is 4x^3, carried down to the left of the - 4x^2; adding down: 4x^3 + (+12x^2) + (-4x^2) + (-12x) + (-7x) + (-21) = 4x^3 + 8x^2 - 19x - 21

    That was a lot easier! But, by either method, the answer is the same:

    4x3 + 8x2 - 19x - 21

    Simplify (x + 2) (x3 + 3x2 + 4x - 17)

    I'm just going to do this one vertically; horizontally is too much trouble.

    Note that, since order doesn't matter for multiplication, I can still put the "x + 2" polynomial on the bottom for the vertical multiplication, just as I always put the smaller number on the bottom when I was doing regular vertical multiplication with just plain numbers back in grammar school.

    x^3 + 3x^2 + 4x - 17 is positioned above x + 2; first row: + 2 times - 17 is - 34, carried down below the + 2; + 2 times + 4x is + 8x, carried down below the x; + 2 times 3x^2 is + 6x^2, carried down to the left of the 8x; + 2 times x^3 is + 2x^3, carried down to the left of the + 6x^2; second row: x times - 17 is - 17x, carried down below the + 8x; x times + 4x is + 4x^2, carried down below the + 6x^2; x times + 3x^2 is + 3x^3, carried down below the + 2x^3; x times x^3 is x^4, carried down to the left of the + 3x^3; adding down: x^4 + (+2x^3) + (3x^3) + (+6x^2) + (+4x^2) + (+8x) + (-17x) + (-34) = x^4 + 5x^3 + 10x^2 - 9x - 34

    x4 + 5x3 + 10x2 - 9x - 34
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “Multiply 3x^2 (5x^3) ...” in 📘 Mathematics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers