Multiply Polynomials 2

Question

Multiply (2x+5)(4x2−2x+3) show what terms you multiplied together. 

Answer 1

Step #1: Distribute all the terms, meaning multiply 2x by each of the three terms, and multiply 5 by each of the three terms as well. So in terms of mathematics, you would obtain,

[(2x*4x^2)+(2x*(-2x))+(2x*3)]+ [(5*4x^2)+(5*(-2x))+(5*3)].

Step #2: Multiply each of the terms. [8x^3-4x^2+6x]+[20x^2-10x+15] When multiplying exponents, you add. For example 5x*6x^3= 30x^4, or 9x^7*8x^3=72x^10. For those that have a variable but not a located exponent, like 2x, always treat as 2x^1, this rule applies for any constant in front of the variable.

Step #3: Finally, combine like expressions and simplify! (This means, whichever terms have the same exponent you add or subtract). So you would add (-4x^2+20x^2=16x^2) and (6x+(-10x)=4x). The other two terms can't be added cause 8x^3 and 15 don't have the same exponent. Therefore,

8x^3+16x^2-4x+15 is your final answer. Order does not matter so you can arrange the terms however you like :)

Answer 2

Answer 3

8x^3 +16x^2 -4x + 15

easiest are the 1st and last terms

just multiply the two highest degreed terms together: 2x times 4x^2 = 8x^3

multiply the two constant terms together: 5 times 3 = 15

the x term of the product is the sum of 5(-2x) and 2x(3) = -10x+6x = -4x

the x^2 term of the product is the sum of 2x(-2x) and 5(4x^2) = -4x^2+20X^2 = 16x^2

then put them altogether in descending order of their powers: 8x^3 + 16x^2 -4x +15

It may be easiest to set it up like long division, where instead of 100th units, 10's unit and 1's units you

have x^2, x, and constant terms

4x^2 -2x + 3

2x + 5

20x^2-10x+15

8x^3-4x^2 + 6x

8x^3 +16x^2-4x +15

multiply similar to arithmetic multiplication

423

25

2115

846

10575

Answer 4

Look from left to right for the first quantity in ().

2x * (4x^2-2x+3) = 8x^3 - 4x + 6x.

Now, distribute 5 through the second quantity in ().

5 * (4x^2-2x+3) = 20x^2 - 10x + 15.

The last step: Add together the two polynomials above.

8x^3 + 20x^2 - 8x + 15.

Answer 5

To multiply (2x+5)(4x2−2x+3) you need to multiply everything in the first by everything in the second. So:

2x (4x²) +2x(-2x) +2x(3) = 8x³ - 4x² + 6x

5(4x²) +5(-2x) + 5(3) = 20x² - 10x +15

Then, combine like terms and simplify:

8x³ + (-4x² + 20x²) + (6x-10x) + 15

8x³ + 16x² -4x + 15

If you need more help with this, feel free to contact me and I can show you other methods of solving!

Answer 6