Question

Help please? this is my last question and i keep getting it wrong.
Multiplying Polynomials
(x2 + 2x - 1)(x2 + 2x + 5)

Answer 1

\(Is~it~(x^{2}+2x-1)(x^{2}+2x+5)~?\)

Answer 2

Yes it is

Answer 3

if that is the case,
(1) we need to multiply each term by term considering the signs of every term, the power exponent of each like term such as x is additive since we are multiplying them, and the resulting product of our constants or coefficients properly in place...
(2) then we combine like terms with respect to the power exponent of x, all \(x^4\) go together, as well as \(x^3\), \(x^2\), \(x\), and the constants...
(3) the result then is the simplified product...

Answer 4

Apply the distributive property:

a(b + c + d) = ab + ac + ad

If we treat (x^2 + 2x - 1) as \(a\)
and treat (x^2 + 2x + 5) as \(b + c + d\)

Then we can apply the distributive property as follows:

Answer 5

(x^2 + 2x - 1)(x^2 + 2x + 5) =
x^2(x^2 + 2x - 1) + 2x(x^2 + 2x - 1) + 5(x^2 + 2x - 1)

Answer 6

i'm out of here, @Hero can handle this... :)

Answer 7

From there, we can continue expanding:
x^2(x^2 + 2x - 1) + 2x(x^2 + 2x - 1) + 5(x^2 + 2x - 1) =
x^4 + 2x^3 - x^2 + 2x^3 + 4x^2 - 2x + 5x^2 + 10x - 5 =
x^4 + 2x^3 + 2x^3 + 4x^2 + 5x^2 - x^2 + 10x - 2x - 5 =
x^4 + (2 + 2)x^3 + (4 + 5 - 1)x^2 + (10 - 2)x - 5 =
x^4 + 4x^3 + 8x^2 + 8x - 5

Answer 8

Sweet, i feel better now about those kind of problems, now that i can see a full explanation of how to do it, thank you for the help @Hero , I got the problem right now (:

Answer 9

and @Orion1213 thankyou for your help aswell. (:

Answer 10

Okay, good luck with it @tswavy