## Podcast Beta

## Questions and Answers

What is meant by 'simplifying' an expression in this context?

To write the expression as the sum of a rational and an irrational number.

What is the identity used to prove that (x + y)(x â€“ y) = xÂ² â€“ yÂ² for any real numbers x and y?

Distributive law of multiplication over addition of real numbers.

What is the significance of 'rationalising' the denominator in a fraction?

To make the denominator a rational number.

On a number line, where does the number âˆš2 lie?

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What is the formula to simplify the expression (a + b)(a - b)?

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What is the purpose of using identities like (a + b)Â² = aÂ² + 2ab + bÂ² in algebraic manipulations?

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What is the benefit of using the distributive law of multiplication over addition of real numbers?

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What is the significance of the identity (a + b)(c + d) = ac + ad + bc + bd?

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What is the difference between a rational and an irrational number?

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How can we simplify an expression like (5 + 7)(2 + 5)?

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