Respuesta :
Product of two polynomials can be done by distribution of multiplication over addition. The product of [tex]-2x^2(x+6)[/tex] is [tex]-2x^3 - 12x^2[/tex]
What is distributive property of multiplication over addition?
Suppose a, b and c are three numbers. Then we have:
[tex]a(b + c) = a\times b + a\times c[/tex]
(a(b+c) means a multiplied to (b+c). The sign of multiplication is usually hidden when using symbols and both quantities which are in multiplication are written together without space)
The product result of the given expression is
[tex]-2x^2(x+6) = -2x^{2+1} -12x^2 =-2x^3 -12x^2[/tex]
It is because when bases are same and there is multiplication, then powers add up, so we have: [tex]a^b \times a^c = a^{b+c}[/tex]
Also, we've
[tex](-ve \times (+ve) = -ve\\(-ve) \times (-ve) = +ve\\(+ve) \times (+ve) = +ve\\(+ve) \times (-ve) = -ve[/tex]
where -ve, +ve are sign of operands and result.
That's why [tex]-2 \times 6 = -12[/tex]
Thus,
The product of [tex]-2x^2(x+6)[/tex] is [tex]-2x^3 - 12x^2[/tex]
Learn more about product of polynomials here:
https://brainly.com/question/9106484
