Asked by Rhetori Thompson on May 10, 2024
Verified
Use a special product pattern to find the product (9x2+8) (9x2−8) \left( 9 x ^ { 2 } + 8 \right) \left( 9 x ^ { 2 } - 8 \right) (9x2+8) (9x2−8) .
A) 81x2−6481 x ^ { 2 } - 6481x2−64
B) 81x2−72x+6481 x ^ { 2 } - 72 x + 6481x2−72x+64
C) 81x4−144x2+6481 x ^ { 4 } - 144 x ^ { 2 } + 6481x4−144x2+64
D) 81x4−17x2−6481 x ^ { 4 } - 17 x ^ { 2 } - 6481x4−17x2−64
E) 81x4−6481 x ^ { 4 } - 6481x4−64
Special Product Pattern
Formulas that provide shortcuts for expanding certain types of binomials or polynomials.
Polynomial
An algebraic expression consisting of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents.
Exponent
A mathematical notation indicating the number of times a number is multiplied by itself.
- Adopt special product schemes to streamline polynomial expression simplification.
Verified Answer
KM
Karina MolinaMay 14, 2024
Final Answer :
E
Explanation :
The given expression is an example of the difference of squares formula, a2−b2=(a+b)(a−b)a^2 - b^2 = (a + b)(a - b)a2−b2=(a+b)(a−b) , where a=9x2a = 9x^2a=9x2 and b=8b = 8b=8 . Therefore, the product is 81x4−6481x^4 - 6481x4−64 .
Learning Objectives
- Adopt special product schemes to streamline polynomial expression simplification.