There are a total of 1225 students at King Middle School. If the population is 52% female, then 1225 x .52 = 637 female. 1225 - 637 = 588 male students.
Answer:
- 8x² + 36xy - 36y²
Step-by-step explanation:
Given
(- 2x + 6y)(4x - 6y)
Each term in the second factor is multiplied by each term in the first factor, that is
- 2x(4x - 6y) + 6y(4x - 6y) ← distribute each parenthesis
= - 8x² + 12xy + 24xy - 36y² ← collect like terms
= - 8x² + 36xy - 36y²
A little bit of trained eyeballing can help here. Let me tell you how I saw the answer without any computation.
Remember that the expansion of a squared binomial is
So, the square of a binomial has the following properties, which you can easily spot:
- It has three terms
- Two of them are perfect squares
- The third is twice the product of the two roots.
Well, in this case we do have three terms, and indeed is the square of 11x, and 1 is the square of itself. The only thing we have to check is that 22x is twice the product of 11x and 1, which is true.
So, the answer is
If you want to see some explicit calculations, just use the quadratic formula
to see that there is a double solution , and then use the formula
to come to the same conclusion.