Respuesta :
Product of two polynomials can be done by distribution of multiplication over addition. The product of [tex](x+5)^2[/tex] is [tex]x^2 + 10x + 25[/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)
What is a polynomial?
They are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.
Example:
[tex]x^3 + 4x + 3[/tex]
is a polynomial.
Using both above facts, as the given expression is [tex](x+5)^2[/tex]
Its product result is obtained as
[tex](x+5)^2 = (x+5)(x+5) = x(x+5) + 5(x+5) = x^{1+1} + 5x + 5x + 25\\\\(x+5)^2 = x^2 + (5+5)x + 25 \text{\:(Addition of coefficients of like terms)}\\\\(x+5)^2 = x^2 + 10x + 25[/tex]
It is a fact that result of a polynomial product is polynomial. Thus, the obtained product is a polynomial since x + 5 was a polynomial.
Thus,
The product of [tex](x+5)^2[/tex] is [tex]x^2 + 10x + 25[/tex]
Learn more about polynomial product here;
https://brainly.com/question/9106484
