- #1
tehmatriks
- 40
- 0
Homework Statement
simplify (2x-3)² - 2x(2x-5).
Homework Equations
The Attempt at a Solution
(2x-3)² - 2x(2x-5)
to
2x² + 9 - 4x² + 10x
to
2x² + 9 + 10x
tiny-tim said:hi tehmatriks!
sorry, but your (2x-3)² is completely wrong
if you can't do it in your head, write it as (2x-3)(2x-3) first, and then expand it
tehmatriks said:thanks, the whole time i was staring at the (2x-3)² and was just thinking about how wrong i was doing it, i always forget that double bracket thing when it comes to these situations, just don't get these much
thanks again man, here's the final result
(2x-3)² - 2x(2x-5)
to
(2x-3)(2x-3) - 2x(2x-5)
to
4x - 6x - 6x + 9 - 4x + 10x
to
9 - 2x
Mark44 said:Use = between expressions that have the same value.
(2x-3)2 - 2x(2x-5)
= (2x-3)(2x-3) - 2x(2x-5) -- so far, so good
After that, things go downhill.
(2x)(2x) = 2*2*x*x = ?
And -2x(2x - 5) = -2x * 2x -2x * (-5) = ?
You have to distribute the -2x over both terms inside the parentheses.
The expression (2x - 3)^2 means to square the quantity (2x - 3), or to multiply it by itself. In other words, it is the same as (2x - 3)(2x - 3), which can be simplified to 4x^2 - 12x + 9.
To simplify this expression, you can use the distributive property to expand the second term, 2x(2x - 5), to get 4x^2 - 10x. Then, you can combine like terms and rewrite the expression as 4x^2 - 12x + 9 - 10x. Finally, you can combine like terms again to get the simplified expression 4x^2 - 22x + 9.
Yes, the expression can be simplified further by factoring out a 2 from the last two terms, giving you 4x^2 - 22x + 9 = 2(2x^2 - 11x + 9). Then, you can further factor the quadratic expression inside the parentheses to get 2(2x - 3)(x - 3). Therefore, the fully simplified expression is 2(2x - 3)(x - 3).
Yes, (2x - 3)^2 - 2x(2x - 5) is a polynomial expression. A polynomial is an algebraic expression that consists of variables and coefficients, combined using addition, subtraction, and multiplication, but no division or square roots. In this case, the expression has two terms, both of which are raised to the second power, making it a polynomial of degree 2.
This expression can be used in various real-life applications, such as calculating the area of a square with side length (2x - 3) and subtracting the area of a rectangle with length 2x and width (2x - 5). It can also represent the profit or loss in a business scenario, where 2x represents the cost of goods sold and (2x - 3)^2 represents the revenue, with an additional loss of 2x(2x - 5).