Questions & Answers: "Expansion Formulae and Algebraic Identities"

Complete guide to "Expansion Formulae and Algebraic Identities" for Math students. Below you will find important questions and model answers to help you prepare.

4 Questions

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Question 1

1 Mark

Which of the two alternative expressions from the given are perfect squares?

Options

$Diagram for Option A$

$Diagram for Option B$

$Diagram for Option C$

$Diagram for Option D$

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Question 2

1 Mark

If $a^{2}+b^{2}=325$ and $a+b=23$ and $ab=102$ Find $(a-b)$ .

Options

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Question 3

1 Mark

Which term should be added to $49x^2+\frac{1}{49x^2}$ to make the expression a complete square. (Choose two correct alternatives.)

Options

-2

-14x

14x

Explanation

To make the expression $49x^2+\frac{1}{49x^2}$ a complete square, we need to add a term that fits the form $(a+b)^2 = a^2 + b^2 + 2ab$ or $(a-b)^2 = a^2 + b^2 - 2ab$ . Here, $a^2 = 49x^2$ , so $a = 7x$ . And $b^2 = \frac{1}{49x^2}$ , so $b = \frac{1}{7x}$ . The term to be added is either $2ab$ or $-2ab$ . $2ab = 2 \times (7x) \times (\frac{1}{7x}) = 2$ . And $-2ab = -2 \times (7x) \times (\frac{1}{7x}) = -2$ . Thus, the terms that can be added are 2 and -2.

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Question 4

1 Mark

Find the value of $\frac{(225)^2-1}{(15)^2+1}$

Options

224

226

326

225

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