-squared.jpeg "(5x-4) Squared")
Understanding (5x - 4)^2
The expression (5x - 4)^2 represents the square of a binomial, meaning it's the product of the binomial with itself. Let's break down how to expand and simplify this expression.
Expanding the Expression
To expand (5x - 4)^2, we can use the FOIL method or the square of a difference formula:
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FOIL method: This stands for First, Outer, Inner, Last. It helps us multiply each term of the first binomial by each term of the second binomial:
- First: (5x) * (5x) = 25x^2
- Outer: (5x) * (-4) = -20x
- Inner: (-4) * (5x) = -20x
- Last: (-4) * (-4) = 16
- Combining like terms: 25x^2 - 20x - 20x + 16 = 25x^2 - 40x + 16
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Square of a difference formula: This formula states: (a - b)^2 = a^2 - 2ab + b^2
- Applying it to our expression: (5x - 4)^2 = (5x)^2 - 2(5x)(4) + (-4)^2
- Simplifying: 25x^2 - 40x + 16
Simplified Form
Therefore, the expanded and simplified form of (5x - 4)^2 is 25x^2 - 40x + 16.
Key Points
- The expression represents a quadratic equation.
- The expansion results in a trinomial (an expression with three terms).
- The first term is the square of the first term of the binomial.
- The second term is twice the product of the first and second term of the binomial.
- The third term is the square of the second term of the binomial.
By understanding how to expand and simplify this type of expression, you can easily solve various algebraic problems involving binomials and quadratic equations.