Practice Algebraic Identities (3.4) - Algebra

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6 sample questions

Question 1.
Expand $(x + 2)^2$ using the square of a sum identity.
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Use the identity $(a + b)^2 = a^2 + 2ab + b^2$.
Question 2.
Simplify $(a - 5)(a + 5)$ using the difference of squares.
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Remember the formula: $a^2 - b^2 = (a-b)(a+b)$.
3Question 3.
What is the result of $(a+b)^2$ ?
- $a^2 + 2ab + b^2$
- $a^2 - 2ab + b^2$
- $(a-b)(a+b)$
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Remember how we expand a squared term.
4Question 4.
True or False: The difference of squares can be expressed as $a^2 + b^2$ .
- True
- False
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Think of the signs involved in the identity.
Question 5.
Prove algebraically that $x^2 - 9$ can be factored as $(x - 3)(x + 3)$ using the difference of squares identity.
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Identify $a$ and $b$ in the expression.
Question 6.
Expand and simplify $(2x + 3)^3$ and express it in standard polynomial form.
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Use $(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$.

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