Algebraic Identities Quiz

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Questions and Answers

What is the value of $(-4ab)^2$?

  • $-16a^2b^2$
  • $-8ab$
  • $8ab$
  • $16a^2b^2$ (correct)

If $(x-3)^2 = 25$, what are the possible values of $x$?

  • $x=8$
  • $x=-5$
  • $x=5$ (correct)
  • $x=-2$

Expand $(2y+3)^2$.

  • $4y^2 - 12y + 9$
  • $4y^2 + 6y + 9$
  • $4y^2 - 6y + 9$
  • $4y^2 + 12y + 9$ (correct)

Simplify $(a+2b)^2 - (a-2b)^2$.

<p>$8a^2 - 8b^2$ (C)</p> Signup and view all the answers

What is the value of $(4c-3)^2$ when $c=2$?

<p>$9$ (A)</p> Signup and view all the answers

Which type of identities form the basis of algebra?

<p>Algebraic identities (B)</p> Signup and view all the answers

What are trigonometric identities distinct from?

<p>Triangle identities (D)</p> Signup and view all the answers

What is the formal symbol for indicating identities?

<p>$=$ (C)</p> Signup and view all the answers

Which type of identities involve certain functions of one or more angles?

<p>Trigonometric identities (C)</p> Signup and view all the answers

What is an identity in mathematics?

<p>An equation relating two mathematical expressions producing the same value for all values of the variables within a certain range of validity (D)</p> Signup and view all the answers

Flashcards

What is $(-4ab)^2$?

Equals $16a^2b^2$. Squaring a term means multiplying it by itself.

If $(x-3)^2 = 25$, what is x?

The possible values of x are 8 and -2.

Expand $(2y+3)^2$.

Expanding $(2y+3)^2$ gives $4y^2 + 12y + 9$.

Simplify $(a+2b)^2 - (a-2b)^2$.

The simplified expression is $8a^2 - 8b^2$.

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Value of $(4c-3)^2$ when $c=2$?

When $c=2$, the value of $(4c-3)^2$ is 25.

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Basis of algebra?

These identities serve as fundamental rules and relationships that underpin various algebraic manipulations and problem-solving techniques.

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Distinct from?

Trigonometric identities differ from triangle identities, as trigonometric identities relate to trigonometric functions and their relationships, whereas triangle identities typically involve side lengths and angles within triangles.

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Symbol for identity?

The formal symbol is denoted by "$" representing that the expressions on either side of the equation are equivalent for all values of the variables.

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Type of identities?

Involve functions like sine, cosine, tangent, etc., applied to angles, establishing relationships and equivalencies between different trigonometric expressions.

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Identity?

Equation relating mathematical expressions, yielding the same value for variable values within a defined validity range.

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