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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

(−5z)−(2−z)⋅(3−z) (-5 z)-(2-z) \cdot(3-z) \newlineWhich of the following expressions is equivalent to the given expression?\newlineChoose 11 answer:\newline(A) −z2−10z−6 -z^{2}-10 z-6 \newline(B) −z2−4z+6 -z^{2}-4 z+6 \newline(C) −z2−6 -z^{2}-6 \newline(D) z2−10z−6 z^{2}-10 z-6

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Full solution

Q. (−5z)−(2−z)⋅(3−z) (-5 z)-(2-z) \cdot(3-z) \newlineWhich of the following expressions is equivalent to the given expression?\newlineChoose 11 answer:\newline(A) −z2−10z−6 -z^{2}-10 z-6 \newline(B) −z2−4z+6 -z^{2}-4 z+6 \newline(C) −z2−6 -z^{2}-6 \newline(D) z2−10z−6 z^{2}-10 z-6
  1. Distribute and expand: Distribute the negative sign through the first term and expand the product of the two binomials.\newlineWe have the expression (−5z)−(2−z)(3−z)(-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-5z. Then we expand the product (2−z)(3−z)(2 - z)(3 - z) using the distributive property (FOIL method).
  2. Apply FOIL method: Apply the FOIL method to the product (2−z)(3−z)(2 - z)(3 - z).
    (2−z)(3−z)=2⋅3+2⋅(−z)+(−z)⋅3+(−z)⋅(−z)(2 - z)(3 - z) = 2 \cdot 3 + 2 \cdot (-z) + (-z) \cdot 3 + (-z) \cdot (-z)
    =6−2z−3z+z2= 6 - 2z - 3z + z^2
    Now, combine like terms.
    =6−5z+z2= 6 - 5z + z^2
  3. Combine like terms: Subtract the expanded binomial from −5z-5z.\newlineNow we have the original expression as:\newline−5z−(6−5z+z2)-5z - (6 - 5z + z^2)\newlineDistribute the negative sign through the parentheses to subtract the binomial.\newline−5z−6+5z−z2-5z - 6 + 5z - z^2
  4. Subtract expanded binomial: Combine like terms.\newlineNow combine the terms −5z-5z and 5z5z, which cancel each other out, and bring down the remaining terms.\newline0z−6−z20z - 6 - z^2\newlineThis simplifies to:\newline−z2−6-z^2 - 6
  5. Simplify expression: Match the simplified expression with the given choices.\newlineThe simplified expression is -z^\(2 - 66＂). Now we compare this with the given choices:\newline(A) -z^{\(2\)}\(-10z−6-6＂)\newline(B) -z^{\(2\)}\(-4z+66＂)\newline(C) -z^{\(2\)}\(-6＂)\newline(D) z^{\(2\)}\(-10z−6-6＂)\newlineThe correct choice that matches our simplified expression is (C) -z^{\(2\)}\(-6＂).

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