%5E2-in-standard-form.jpeg "(x-5)^2 In Standard Form")
Expanding (x-5)^2 in Standard Form
In algebra, expanding expressions involving parentheses and exponents is a crucial skill to master. One such expression is (x-5)^2, which can be expanded into a quadratic expression in standard form. In this article, we will explore how to expand (x-5)^2 using the exponent rule and simplify the resulting expression.
The Exponent Rule
The exponent rule states that when an expression is raised to a power, each term within the expression must be raised to that power. In the case of (x-5)^2, we need to raise both x and -5 to the power of 2.
Expanding (x-5)^2
Using the exponent rule, we can expand (x-5)^2 as follows:
(x-5)^2 = (x-5)(x-5)
= x(x) - x(5) - 5(x) + (-5)(-5)
= x^2 - 5x - 5x + 25
Simplifying the Expression
Now, let's simplify the expression by combining like terms:
= x^2 - 10x + 25
Standard Form
The expression x^2 - 10x + 25 is in standard form, also known as the quadratic form. In standard form, a quadratic expression is written as:
ax^2 + bx + c
where a, b, and c are constants, and a ≠ 0.
Conclusion
In this article, we have successfully expanded (x-5)^2 into a quadratic expression in standard form: x^2 - 10x + 25. Remember to apply the exponent rule and simplify the expression by combining like terms to obtain the final result.
