Q. Expand.Your answer should be a polynomial in standard form.(9b−1)(9b+1)=
Recognize the pattern: Recognize the pattern in the expression (9b−1)(9b+1).This expression is a difference of squares, which follows the pattern (a−b)(a+b)=a2−b2.
Apply the difference of squares formula: Apply the difference of squares formula.Here, a is 9b and b is 1. So, we have:(9b−1)(9b+1)=(9b)2−(1)2
Calculate the squares: Calculate the squares of 9b and 1.(9b)2=81b2(1)2=1
Subtract the squares: Subtract the square of 1 from the square of 9b.81b2−1
Write the final answer in standard form: Write the final answer in standard form.The standard form of a polynomial is written with the highest degree term first, followed by lower degree terms in descending order. Since we only have one term with b and a constant term, the standard form is:81b2−1