Asked by Lesley Horcasitas on Apr 29, 2024
Verified
Multiply (x2+4x−4) (5x2+2) \left( x ^ { 2 } + 4 x - 4 \right) \left( 5 x ^ { 2 } + 2 \right) (x2+4x−4) (5x2+2) and simplify.
A) 5x4+8x−85 x ^ { 4 } + 8 x - 85x4+8x−8
B) 5x4+24x3+8x−85 x ^ { 4 } + 24 x ^ { 3 } + 8 x - 85x4+24x3+8x−8
C) 5x4+20x3−18x2+8x−85 x ^ { 4 } + 20 x ^ { 3 } - 18 x ^ { 2 } + 8 x - 85x4+20x3−18x2+8x−8
D) 5x4+20x3+2x2−85 x ^ { 4 } + 20 x ^ { 3 } + 2 x ^ { 2 } - 85x4+20x3+2x2−8
E) 5x4+24x3−20x2+8x−85 x ^ { 4 } + 24 x ^ { 3 } - 20 x ^ { 2 } + 8 x - 85x4+24x3−20x2+8x−8
Multiply
The arithmetic operation of scaling one number by another, equivalent to adding a number to itself multiple times.
Simplify
The process of reducing a mathematical expression or equation to its simplest form.
- Employ the patterns associated with special products in the simplification of polynomial expressions.
Verified Answer
ZK
Zybrea Knight
May 03, 2024
Final Answer :
C
Explanation :
Multiplying the two polynomials: (x2+4x−4)(5x2+2)=5x4+20x3−20x2+8x−8 (x^2 + 4x - 4)(5x^2 + 2) = 5x^4 + 20x^3 - 20x^2 + 8x - 8 (x2+4x−4)(5x2+2)=5x4+20x3−20x2+8x−8 , which simplifies to the expression in choice C.
Learning Objectives
- Employ the patterns associated with special products in the simplification of polynomial expressions.