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We want to factor the following expression: 3x^(2)-16y^(5) Which pattern can we use to factor the expression? U and V are either constant integers or single-variable expressions. Choose 1 answer: (A) (U+V)^(2) or (U-V)^(2) (B) (U+V)(U-V) (c) We can't use any of the patterns.

We want to factor the following expression:\newline3x2−16y5 3 x^{2}-16 y^{5} \newlineWhich pattern can we use to factor the expression?\newlineU U and V V are either constant integers or single-variable expressions.\newlineChoose 11 answer:\newline(A) (U+V)2 (U+V)^{2} or (U−V)2 (U-V)^{2} \newline(B) (U+V)(U−V) (U+V)(U-V) \newline(C) We can't use any of the patterns.

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Q. We want to factor the following expression:\newline3x2−16y5 3 x^{2}-16 y^{5} \newlineWhich pattern can we use to factor the expression?\newlineU U and V V are either constant integers or single-variable expressions.\newlineChoose 11 answer:\newline(A) (U+V)2 (U+V)^{2} or (U−V)2 (U-V)^{2} \newline(B) (U+V)(U−V) (U+V)(U-V) \newline(C) We can't use any of the patterns.
  1. Analyze expression for factoring patterns: Analyze the given expression to determine if it fits any common factoring patterns.\newlineThe given expression is 3x2−16y53x^2 - 16y^5. We need to check if this expression fits any of the provided patterns: (U+V)2(U+V)^2, (U−V)2(U-V)^2, or (U+V)(U−V)(U+V)(U-V).
  2. Check for difference of squares pattern: Check if the expression is a difference of squares.\newlineThe difference of squares pattern is (U2−V2)=(U+V)(U−V)(U^2 - V^2) = (U + V)(U - V). For the given expression 3x2−16y53x^2 - 16y^5 to fit this pattern, both terms would need to be perfect squares. However, 3x23x^2 is not a perfect square because 33 is not a square number, and 16y516y^5 is not a perfect square because the exponent 55 is not even. Therefore, the expression does not fit the difference of squares pattern.
  3. Check for perfect square trinomial: Check if the expression is a perfect square trinomial.\newlineThe perfect square trinomial patterns are (U+V)2(U+V)^2 and (U−V)2(U-V)^2. These patterns result in trinomials, but our expression is a binomial with only two terms. Therefore, the expression does not fit either of the perfect square trinomial patterns.
  4. Determine if other factoring patterns apply: Determine if any other factoring patterns apply.\newlineSince the expression does not fit the difference of squares pattern or the perfect square trinomial patterns, and there are no common factors between 3x23x^2 and 16y516y^5, we conclude that none of the provided patterns can be used to factor the expression.

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