Fully factorise u² - 64
Understand the Problem
The question is asking to fully factor the expression u² - 64, which is a difference of squares. To solve it, we will identify the square roots and apply the difference of squares formula.
Answer
$$(u - 8)(u + 8)$$
Answer for screen readers
The fully factored expression is $$(u - 8)(u + 8)$$.
Steps to Solve
-
Identify the expression
We start with the expression: $u^2 - 64$. -
Recognize the difference of squares
This expression can be recognized as a difference of squares. The difference of squares formula states that $a^2 - b^2 = (a - b)(a + b)$. -
Determine the values of a and b
Here, $a = u$ and $b = 8$ because $64 = 8^2$. -
Apply the difference of squares formula
We can apply the formula: $$u^2 - 64 = (u - 8)(u + 8)$$ -
Final expression
The fully factored form of the expression is: $$(u - 8)(u + 8)$$
The fully factored expression is $$(u - 8)(u + 8)$$.
More Information
This expression showcases the difference of squares, which is a common factorization technique applicable in algebra. Recognizing this pattern can simplify quadratic expressions effectively.
Tips
- Overlooking the perfect squares: Sometimes, students forget to identify that $64$ is a perfect square. It’s important to check if both terms in a difference are perfect squares.
- Incorrect application of the formula: Students might confuse the formula and apply it incorrectly, leading to mistakes in signs or terms.
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