We want to factor the following expression: x^(3)-25 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 expression type: We need to recognize the type of expression we are dealing with. The expression x^3 - 25 is a difference of two cubes because x^3 is a cube of x and 25 is a cube of 5. The difference of two cubes can be factored using the formula a^3 - b^3 = (a - b)(a^2 + ab + b^2), where a and b are any expressions. In our case, a = x and b = 5.Apply difference of cubes formula: Now we apply the difference of cubes formula to the expression x^3 - 25. We have a = x and b = 5, so the factored form will be (x - 5)(x^2 + 5x + 25).Check factored form: We can check our work by expanding the factored form to see if it equals the original expression. (x - 5)(x^2 + 5x + 25) = x^3 + 5x^2 + 25x - 5x^2 - 25x - 125. Simplifying this, we get x^3 - 125, which is not equal to the original expression x^3 - 25. This indicates that we made a mistake in our calculation.

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We want to factor the following expression:

x^(3)-25
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: $\newline$ $x^{3}-25$ $\newline$ 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^{3}-25

\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 expression type: We need to recognize the type of expression we are dealing with. The expression $x^3 - 25$ is a difference of two cubes because $x^3$ is a cube of $x$ and $25$ is a cube of $5$ . The difference of two cubes can be factored using the formula $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$ , where $a$ and $b$ are any expressions. In our case, $a = x$ and $b = 5$ .
Apply difference of cubes formula: Now we apply the difference of cubes formula to the expression $x^3 - 25$ . We have $a = x$ and $b = 5$ , so the factored form will be $(x - 5)(x^2 + 5x + 25)$ .
Check factored form: We can check our work by expanding the factored form to see if it equals the original expression. $(x - 5)(x^2 + 5x + 25) = x^3 + 5x^2 + 25x - 5x^2 - 25x - 125$ . Simplifying this, we get $x^3 - 125$ , which is not equal to the original expression $x^3 - 25$ . This indicates that we made a mistake in our calculation.