Product of two polynomials can be done by distribution of multiplication over addition. The product of [tex](x-3)^2[/tex] is [tex]x^2 - 6x + 9[/tex]
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)
For the given case, the product needed can be calculated as:
[tex](x-3)^2 = (x-3) \times(x-3) = x(x-3) - 3(x-3) = x^2 - 3x - 3x + 9\\\\(x-3)^2 = x^2 - (3+3)x + 9 = x^2 - 6x + 9[/tex]
(coefficients of like terms were added)
Thus, the product result of given expression is
[tex]x^2 - 6x + 9[/tex]
Learn more about product of polynomials here:
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