Which of the following is equivalent to x(x-1) ? Choose 1 answer: (A) 2x-1 (B) x^(2)-x (c) x^(2)-1 (D) 2x^(2)-x

Expand using distributive property: We need to expand the expression x(x-1) by using the distributive property, which states that a(b + c) = ab + ac. Here, we can think of x as 'a' and (x-1) as (b + c) where b = x and c = -1. So, x(x-1) = x*x + x*(-1) = x^2 - x.Compare with given choices: Now, let's compare the expanded expression x^2 - x with the given choices to find the equivalent expression. (A) 2x-1 is not equivalent because it does not match x^2 - x. (B) x^2 - x is equivalent because it is exactly the same as the expanded expression. (C) x^2 - 1 is not equivalent because it does not have the -x term. (D) 2x^2 - x is not equivalent because the coefficient of x^2 is 2, not 1 as in the expanded expression.

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Which of the following is equivalent to
x(x-1) ?
Choose 1 answer:
(A)
2x-1
(B)
x^(2)-x
(c)
x^(2)-1
(D)
2x^(2)-x

Which of the following is equivalent to $x(x-1)$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $2 x-1$ $\newline$ (B) $x^{2}-x$ $\newline$ (C) $x^{2}-1$ $\newline$ (D) $2 x^{2}-x$

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Math Problems

Algebra 1

Compare linear and exponential growth

Full solution

Q. Which of the following is equivalent to

x(x-1)

\newline

Choose

1

answer:

\newline

(A)

2 x-1

\newline

(B)

x^{2}-x

\newline

(C)

x^{2}-1

\newline

(D)

2 x^{2}-x

Expand using distributive property: We need to expand the expression $x(x-1)$ by using the distributive property, which states that $a(b + c) = ab + ac$ . Here, we can think of $x$ as ' $a$ ' and $(x-1)$ as $(b + c)$ where $b = x$ and $c = -1$ . So, $x(x-1) = x\times x + x\times (-1) = x^2 - x$ .
Compare with given choices: Now, let's compare the expanded expression $x^2 - x$ with the given choices to find the equivalent expression. $\newline$ (A) $2x-1$ is not equivalent because it does not match $x^2 - x$ . $\newline$ (B) $x^2 - x$ is equivalent because it is exactly the same as the expanded expression. $\newline$ (C) $x^2 - 1$ is not equivalent because it does not have the $-x$ term. $\newline$ (D) $2x^2 - x$ is not equivalent because the coefficient of $x^2$ is $2$ , not $1$ as in the expanded expression.