There are (4f - 5)^2 workers in a field harvesting strawberries. How many workers are in the field? Expand the expression and simplify.

Question

I don't know how to solve this or expand expressions, please help.

Answer 1

All students in Algebra  the way to square a binomial: (A ± B)² = A² ±2AB + B²

 

and all good students use this pattern to square binomials properly.  Having to use FOIL in this instance is not the best policy; it's like reinventing the wheel each time. Students who don't learn & understand this as the ones who cannot do well on timed tests such as SAT, and still flounder in algebraic work in trigonometry & calculus courses.

 

Squaring a binomial always creates a trinomial, and the middle term always consists of all four parts together: ± 2 A B

Answer 2

(4f - 5)²

(4f)² - 5(4f) - 5(4f) + 5²       FOIL

16f² - 40f + 25

Answer 3

Pixie,

 

There are two ways to do this problem. If you know the Binomial Theorem, you can use it to expand any binomial raised to a power. If you do not, the only way to do this is by brute-force multiplication, meaning you need to multiply (4f − 5) by itself four times and simplify along the way.

 

Before I show you how to do this, let me know if you have learned the Binomial Theorem. If you need help understanding it, I can help with this too. If you have not been taught this, I will show you the slower method.