Find the product of the binomial? (x3 - 3x)(5x2 + 2)

Question

whpalmer4 · Answer

Okay, to multiply polynomials like this, just remember that each part of the first polynomial multiplies each part of the second polynomial.  Then collect like terms to simplify.

For example:

$$(x^2 - 2x)(x + 4) = x^2(x+4) - 2x(x+4) $$$$= x^2*x + x^2*4 - 2x*x -2x*4 $$$$= x^3+4x^2-2x^2-8x$$$$=x^3+2x^2-8x $$

whpalmer4 · Answer

You are just using the distributive property of multiplication over and over...

anonymous · Answer

Can you multiply x^3 and 5x^2 together? @whpalmer4

whpalmer4 · Answer

Yes, of course. $$ x^3 * 5x^2 = 5 * x^3 * x^2 = 5 * (x*x*x) * (x*x)= 5x^5$$

whpalmer4 · Answer

By the properties of exponents, $$x^n*x^m = x^{n+m}$$

whpalmer4 · Answer

But they have to have the same base — you can't do 
$$x^3*y^2 = x^5$$ or anything like that.  

$$x^3*y^2 = x^3y^2$$