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.

Recognize difference of squares: We are given the expression (x+1)^(2)-4y^(2) and we need to identify the pattern that can be used to factor it. Let's first recognize that this expression is a difference of squares.Identify a and b: A difference of squares is an expression of the form a^2 - b^2, which can be factored into (a + b)(a - b). In our case, we can write (x+1)^(2) as a^2 and 4y^(2) as b^2.Apply factoring pattern: Now, let's identify a and b in our expression. We have a = (x+1) and b = 2y because (2y)^2 = 4y^2.Factor the expression: Using the difference of squares pattern, we can factor the expression as follows: (x+1)^(2) - 4y^(2) = (a + b)(a - b) = ((x+1) + 2y)((x+1) - 2y).Use U+V and U-V: This shows that we can use the pattern (U+V)(U-V) to factor the expression, where U = (x+1) and V = 2y.

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We want to factor the following expression: $\newline$ $(x+1)^{2}-4y^{2}$ $\newline$ Which pattern can we use to factor the expression? $\newline$ $U$ and $V$ are either constant integers or single-variable expressions. $\newline$ Choose $1$ answer: $\newline$ (A) $(U+V)^{2}$ or $(U-V)^{2}$ $\newline$ (B) $(U+V)(U-V)$ $\newline$ (C) We can't use any of the patterns.

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Q. We want to factor the following expression:

\newline

(x+1)^{2}-4y^{2}

\newline

Which pattern can we use to factor the expression?

\newline

U

and

V

are either constant integers or single-variable expressions.

\newline

Choose

1

answer:

\newline

(A)

(U+V)^{2}

(U-V)^{2}

\newline

(B)

(U+V)(U-V)

\newline

Recognize difference of squares: We are given the expression $(x+1)^{2}-4y^{2}$ and we need to identify the pattern that can be used to factor it. Let's first recognize that this expression is a difference of squares.
Identify $a$ and $b$ : A difference of squares is an expression of the form $a^2 - b^2$ , which can be factored into $(a + b)(a - b)$ . In our case, we can write $(x+1)^{2}$ as $a^2$ and $4y^{2}$ as $b^2$ .
Apply factoring pattern: Now, let's identify $a$ and $b$ in our expression. We have $a = (x+1)$ and $b = 2y$ because $(2y)^2 = 4y^2$ .
Factor the expression: Using the difference of squares pattern, we can factor the expression as follows: $(x+1)^{2} - 4y^{2} = (a + b)(a - b) = ((x+1) + 2y)((x+1) - 2y)$ .
Use $U+V$ and $U-V$ : This shows that we can use the pattern $(U+V)(U-V)$ to factor the expression, where $U = (x+1)$ and $V = 2y$ .