(-5z)-(2-z)*(3-z) Which of the following expressions is equivalent to the given expression? Choose 1 answer: (A) -z^(2)-10 z-6 (B) -z^(2)-4z+6 (c) -z^(2)-6 (D) z^(2)-10 z-6

Distribute and expand: Distribute the negative sign through the first term and expand the product of the two binomials. We have the expression (-5z) - (2 - z)(3 - z). First, we distribute the negative sign through the first term, which does not change anything since it's just -5z. Then we expand the product (2 - z)(3 - z) using the distributive property (FOIL method).Apply FOIL method: Apply the FOIL method to the product (2 - z)(3 - z). (2 - z)(3 - z) = 2*3 + 2*(-z) + (-z)*3 + (-z)*(-z) = 6 - 2z - 3z + z^2 Now, combine like terms. = 6 - 5z + z^2Combine like terms: Subtract the expanded binomial from -5z. Now we have the original expression as: -5z - (6 - 5z + z^2) Distribute the negative sign through the parentheses to subtract the binomial. -5z - 6 + 5z - z^2Subtract expanded binomial: Combine like terms. Now combine the terms -5z and 5z, which cancel each other out, and bring down the remaining terms. 0z - 6 - z^2 This simplifies to: -z^2 - 6Simplify expression: Match the simplified expression with the given choices. The simplified expression is -z^2 - 6. Now we compare this with the given choices: (A) -z^(2)-10 z-6 (B) -z^(2)-4z+6 (C) -z^(2)-6 (D) z^(2)-10 z-6 The correct choice that matches our simplified expression is (C) -z^(2)-6.

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(-5z)-(2-z)*(3-z)
Which of the following expressions is equivalent to the given expression?
Choose 1 answer:
(A)
-z^(2)-10 z-6
(B)
-z^(2)-4z+6
(c)
-z^(2)-6
(D)
z^(2)-10 z-6

$(-5 z)-(2-z) \cdot(3-z)$ $\newline$ Which of the following expressions is equivalent to the given expression? $\newline$ Choose $1$ answer: $\newline$ (A) $-z^{2}-10 z-6$ $\newline$ (B) $-z^{2}-4 z+6$ $\newline$ (C) $-z^{2}-6$ $\newline$ (D) $z^{2}-10 z-6$

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Math Problems

Algebra 1

Compare linear and exponential growth

Full solution

(-5 z)-(2-z) \cdot(3-z)

\newline

Which of the following expressions is equivalent to the given expression?

\newline

Choose

1

answer:

\newline

(A)

-z^{2}-10 z-6

\newline

(B)

-z^{2}-4 z+6

\newline

(C)

-z^{2}-6

\newline

(D)

z^{2}-10 z-6

Distribute and expand: Distribute the negative sign through the first term and expand the product of the two binomials. $\newline$ We have the expression $(-5z) - (2 - z)(3 - z)$ . First, we distribute the negative sign through the first term, which does not change anything since it's just $-5z$ . Then we expand the product $(2 - z)(3 - z)$ using the distributive property (FOIL method).
Apply FOIL method: Apply the FOIL method to the product $(2 - z)(3 - z)$ .
$(2 - z)(3 - z) = 2 \cdot 3 + 2 \cdot (-z) + (-z) \cdot 3 + (-z) \cdot (-z)$
$= 6 - 2z - 3z + z^2$
Now, combine like terms.
$= 6 - 5z + z^2$
Combine like terms: Subtract the expanded binomial from $-5z$ . $\newline$ Now we have the original expression as: $\newline$ $-5z - (6 - 5z + z^2)$ $\newline$ Distribute the negative sign through the parentheses to subtract the binomial. $\newline$ $-5z - 6 + 5z - z^2$
Subtract expanded binomial: Combine like terms. $\newline$ Now combine the terms $-5z$ and $5z$ , which cancel each other out, and bring down the remaining terms. $\newline$ $0z - 6 - z^2$ $\newline$ This simplifies to: $\newline$ $-z^2 - 6$
Simplify expression: Match the simplified expression with the given choices. $\newline$ The simplified expression is -z^$2 - $6$ ＂). Now we compare this with the given choices: $\newline$ (A) -z^{\(2$}$-10z $-6$ ＂) $\newline$ (B) -z^{\(2$}$-4z+ $6$ ＂) $\newline$ (C) -z^{\(2$}$-6＂) $\newline$ (D) z^{\(2$}$-10z $-6$ ＂) $\newline$ The correct choice that matches our simplified expression is (C) -z^{\(2$}\(-6＂).