Respuesta :
The term b^2 / 4a^2 is not added to the left side of the equation, because the term that was added to the right was not either b^2 / 4 a^2.
As you can see the ther b^2 / 4a^2 that appears in the last step of the table is inside a parenthesis, which is preceded by factor a.
Then, you need to apply the distributive property to know the term that you are really adding to the right side, i.e. you need to mulitply b^2 / 4a^2 * a which is b^2 / 4a.
That means that you are really adding b^2 / 4a to the right, so that is the same that you have to add to the left, which is what the last step of the table shows.
That situation is reflected by the statement "The distributive property needs to be applied to determine the value to add to the left side of the equation to balance the sides of the equation". That is the answer.
As you can see the ther b^2 / 4a^2 that appears in the last step of the table is inside a parenthesis, which is preceded by factor a.
Then, you need to apply the distributive property to know the term that you are really adding to the right side, i.e. you need to mulitply b^2 / 4a^2 * a which is b^2 / 4a.
That means that you are really adding b^2 / 4a to the right, so that is the same that you have to add to the left, which is what the last step of the table shows.
That situation is reflected by the statement "The distributive property needs to be applied to determine the value to add to the left side of the equation to balance the sides of the equation". That is the answer.
In the first few steps for deriving the quadratic formula left side of the equation due to the distributive property for balancing the equation.
What is quadratic equation?
A quadratic equation is the equation in which the highest power of the variable is two.
The first few steps in deriving the quadratic formula are shown in the table.
Use the substitution property of equality to solve it further,
-c=-ax² +bx
Now factor out the term a, to solve further as,
[tex]-c=a(x^2+\dfrac{b}{a}x)[/tex]
Find half of the b value and square it to determine the constant of the perfect square trinomial as,
[tex](\dfrac{b}{2a})^2= \dfrac{b^2}{4a^2}[/tex]
Now the distributive property needs to be applied to determine the value to add to the left side of the equation to balance the sides of the equation.
[tex]-c+\dfrac{b^2}{4a^2}=a(x^2+\dfrac{b}{a}x+\dfrac{b^2}{4a^2})[/tex]
Hence, the distributive property needs to be applied to determine the value to add to the left side of the equation to balance the sides of the equation.
Learn more about the quadratic equation here;
https://brainly.com/question/17177510
