Asked by Sofia Mateeva on May 09, 2024
Verified
Use a special product pattern to find the product (x+9) (x−9) ( x + 9 ) ( x - 9 ) (x+9) (x−9) .
A) x2−18x+81x ^ { 2 } - 18 x + 81x2−18x+81
B) x2−81x ^ { 2 } - 81x2−81
C) x2+81x ^ { 2 } + 81x2+81
D) x2+18x+81x ^ { 2 } + 18 x + 81x2+18x+81
E) x2−18x ^ { 2 } - 18x2−18
Special Product Pattern
Mathematical formulas that quickly solve specific types of polynomial multiplication problems.
Polynomial
A mathematical expression consisting of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
- Apply special product patterns to simplify polynomial expressions.
Verified Answer
LH
LINDA HENDERSONMay 10, 2024
Final Answer :
B
Explanation :
This problem can be solved using the formula (a+b)(a−b)=a2−b2(a+b)(a-b) = a^2 - b^2(a+b)(a−b)=a2−b2 . If we let a=xa=xa=x and b=9b=9b=9 , we get:
(x+9)(x−9)=x2−92=x2−81(x+9)(x-9) = x^2 - 9^2 = x^2 - 81(x+9)(x−9)=x2−92=x2−81
Therefore, the correct answer is B.
(x+9)(x−9)=x2−92=x2−81(x+9)(x-9) = x^2 - 9^2 = x^2 - 81(x+9)(x−9)=x2−92=x2−81
Therefore, the correct answer is B.
Learning Objectives
- Apply special product patterns to simplify polynomial expressions.