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(x – a (x + a) =?
- a)x2+ a2
- b)x −− a2
- c)x2−− a2
- d)x + a2
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
(x – a (x + a) =?a)x2+a2b)x−−a2c)x2−−a2d...
(a-b)(a+b) = a^2 - b^2(x-a)(x+a) = x (x+a) -a (x+a) = x^2 + ax -ax -a^2 = x^2 - a ^2
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(x – a (x + a) =?a)x2+a2b)x−−a2c)x2−−a2d...
Understanding the Expression
The expression given is (x − a)(x + a). This is a product of two binomials, which can be simplified using the distributive property or recognizing it as a difference of squares.
Applying the Difference of Squares Formula
The formula for the difference of squares states that:
- (p − q)(p + q) = p² − q²
Here, if we let p = x and q = a, we can apply the formula directly:
- (x − a)(x + a) = x² − a²
Breaking Down the Steps
- Step 1: Identify the terms:
- p = x
- q = a
- Step 2: Apply the difference of squares:
- Using the formula, substitute p and q:
- (x − a)(x + a) = x² − a²
Conclusion
Thus, the expression simplifies to x² − a², which matches option 'C'.
- Key Insight: This property is particularly useful in algebra for simplifying expressions and solving equations.
Final Answer
The correct answer is option 'C': x² − a².
The expression given is (x − a)(x + a). This is a product of two binomials, which can be simplified using the distributive property or recognizing it as a difference of squares.
Applying the Difference of Squares Formula
The formula for the difference of squares states that:
- (p − q)(p + q) = p² − q²
Here, if we let p = x and q = a, we can apply the formula directly:
- (x − a)(x + a) = x² − a²
Breaking Down the Steps
- Step 1: Identify the terms:
- p = x
- q = a
- Step 2: Apply the difference of squares:
- Using the formula, substitute p and q:
- (x − a)(x + a) = x² − a²
Conclusion
Thus, the expression simplifies to x² − a², which matches option 'C'.
- Key Insight: This property is particularly useful in algebra for simplifying expressions and solving equations.
Final Answer
The correct answer is option 'C': x² − a².
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