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Mathematics
Algebraic Expressions
Factorization: Perfect Cube Form
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Multiple Choice
What is the expanded form of $(a - b)^3$?
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$a^3 - 3a^2b + 3ab^2 - b^3$
$a^3 + 3a^2b - 3ab^2 + b^3$
$a^3 - b^3$
$a^2 - 2ab + b^2$
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Identify the pattern used to factor $64x^3 + 96x^2y + 48xy^2 + 8y^3$.
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$(4x + 2y)^3$
$(4x - 2y)^3$
$(8x + y)^3$
$(2x + 4y)^3$
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What is the correct expansion for $(2a + 3b)^3$?
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$8a^3 + 36a^2b + 54ab^2 + 27b^3$
$8a^3 + 12a^2b + 18ab^2 + 27b^3$
$8a^3 + 24a^2b + 36ab^2 + 27b^3$
$8a^3 + 24a^2b + 54ab^2 + 27b^3$
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Which formula corresponds to the expression $a^3 + 3a^2b + 3ab^2 + b^3$?
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$(a - b)^3$
$(a + b)^3$
$(a + b)^2$
$a^3 + b^3$
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Which formula is used to expand $(x + y)^3$?
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$(x + y)^3 = x^3 + y^3$
$(x + y)^3 = x^3 + 3x^2y + 3xy^2 + y^3$
$(x + y)^3 = x^3 + 3xy + y^3$
$(x + y)^3 = x^2 + 2xy + y^2$
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