Respuesta :
Product of polynomials can be done by distribution of multiplication over addition. The product of [tex](2x - 3)(2x^2 + 7x - 1)[/tex] is [tex]4x^3 + 8x^2 -23x + 3[/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 - 3)(2x^2 + 7x - 1) = 2x(2x^2 + 7x - 1) -3(2x^2 + 7x - 1) \\(2x - 3)(2x^2 + 7x - 1) = 4x^{1+2} + 14x^2 -2x - 6x^2 - 21x + 3\\(2x - 3)(2x^2 + 7x - 1) = 4x^3 + (14 -6)x^2 + (-2 -21)x + 3\\(2x - 3)(2x^2 + 7x - 1) = 4x^3 + 8x^2 -23x + 3[/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 -1 = -2[/tex]
Thus,
The product of [tex](2x - 3)(2x^2 + 7x - 1)[/tex] is [tex]4x^3 + 8x^2 -23x + 3[/tex]
Learn more about product of polynomials here:
https://brainly.com/question/9106484
