- #1
TheePhysicsStudent
- 19
- 16
- Homework Statement
- I understand everything before and after this line but not sure how they actually came to that conclusion, many thanks.
- Relevant Equations
- ax^4 + bx^3 + cx^2 + dx + 3
In this step of the solution, the equation is being simplified using the properties of exponents. Any number raised to the power of 1 is equal to the number itself, so (1)^2 = 1 and (-3)^2 = 9. Therefore, a x (1)^2 x (-3)^2 simplifies to a x 1 x 9, which equals 9a.
The equation simplifies to 3 = a x (1)^2 x (-3)^2 by substituting the values of (1)^2 and (-3)^2 into the equation. Since (1)^2 equals 1 and (-3)^2 equals 9, the equation simplifies to 3 = a x 1 x 9, which can be further simplified to 3 = 9a.
The mathematical rule applied to simplify a x (1)^2 x (-3)^2 to 3 = a x (1)^2 x (-3)^2 is the rule of exponents. When a number is raised to the power of 1, it remains the same. Therefore, (1)^2 equals 1 and (-3)^2 equals 9, resulting in the simplified equation 3 = a x 1 x 9, which simplifies to 3 = 9a.
The value of a is not explicitly shown in the equation 3 = a x (1)^2 x (-3)^2 because it is being treated as a constant coefficient that is being multiplied by the terms (1)^2 and (-3)^2. By simplifying the equation, we can determine the value of a, which in this case would be a = 3/9 or a = 1/3.
The simplification of a x (1)^2 x (-3)^2 to 3 = a x (1)^2 x (-3)^2 is a crucial step in solving the equation as it helps in reducing the complexity of the expression. By simplifying the