Perform and give answer in simplified form
Find the product
(2x-5)^2
(2x-5)^2 or (2x-5)(2x-5)
= 4x^2 - 10x - 10x + 25
= 4x^2 - 20x + 25
after doing several of these, you should be able to jump to the final answer in one step.
To find the product, expand the given expression, which is a binomial squared. Here's how you can do it step by step:
1. Start with the given expression: (2x - 5)^2
2. Apply the formula for squaring a binomial: (a - b)^2 = a^2 - 2ab + b^2, where "a" represents the first term and "b" represents the second term.
3. Substitute "2x" for "a" and "-5" for "b" in the formula: (2x)^2 - 2(2x)(-5) + (-5)^2
4. Simplify each term separately:
- (2x)^2 = (2x)(2x) = 4x^2 (multiplying the coefficients and adding the exponents)
- 2(2x)(-5) = -20x (multiplying the coefficients and variables, and considering the negative sign)
- (-5)^2 = (-5)(-5) = 25 (multiplying the coefficients)
5. Combine the simplified terms: 4x^2 - 20x + 25
So, the product of (2x - 5)^2 is 4x^2 - 20x + 25, in simplified form.