y=3x+10
Which expression should be added to Y so that :
y=(x−4)2
To solve this problem, we will follow these steps:
- Step 1: Expand the expression (x−4)2.
- Step 2: Compare the expanded quadratic expression with 3x+10.
- Step 3: Determine the additional expression needed.
Let's carry out these steps:
Step 1: First, expand (x−4)2. Using the formula for the square of a binomial, we have:
(x−4)2=x2−2⋅x⋅4+42
This simplifies to:
x2−8x+16
Step 2: We need to convert y=3x+10 into this expanded form. That means 3x+10 should become x2−8x+16.
Step 3: The expression to add is the difference between x2−8x+16 and 3x+10:
Subtract 3x+10 from x2−8x+16:
(x2−8x+16)−(3x+10)
This simplifies to:
x2−8x+16−3x−10=x2−11x+6
Therefore, the expression that should be added to y is x2−11x+6.
x2−11x+6