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We want to factor the following expression: (x+1)^(2)-4y^(2) 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:\newline(x+1)2−4y2 (x+1)^{2}-4 y^{2} \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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Full solution

Q. We want to factor the following expression:\newline(x+1)2−4y2 (x+1)^{2}-4 y^{2} \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. Recognize Pattern: Recognize the pattern in the expression.\newlineThe expression (x+1)2−4y2(x+1)^{2}-4y^{2} resembles the difference of squares pattern, which is a2−b2=(a+b)(a−b)a^{2} - b^{2} = (a + b)(a - b).
  2. Identify aa and bb: Identify 'aa' and 'bb' in the pattern.\newlineIn the expression (x+1)2−4y2(x+1)^{2}-4y^{2}, 'aa' is (x+1)(x+1) and 'bb' is 2y2y because (2y)2=4y2(2y)^{2} = 4y^{2}.
  3. Apply Difference of Squares: Apply the difference of squares pattern.\newlineUsing the pattern a2−b2=(a+b)(a−b)a^2 - b^2 = (a + b)(a - b), we can factor the expression as follows:\newline(x+1)2−4y2=[(x+1)+2y]∗[(x+1)−2y](x+1)^{2}-4y^{2} = [(x+1) + 2y] * [(x+1) - 2y].
  4. Write Factored Form: Write the factored form.\newlineThe factored form of the expression is (x+1+2y)(x+1−2y)(x+1 + 2y)(x+1 - 2y).

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