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Which expression below simplifies to (2(z^(2)-2))/(3w^(2)) ? A. ((4w^(2)z^(4)-16w^(2)z^(2)))/(9w^(6)z^(4)) B. ((4w^(2)z^(4)-16w^(2)z^(2)))/(9w^(4)z^(2)) C. ((12w^(2)z^(4)-24w^(2)z^(2)))/(18w^(6)z^(4)) (D. ((12w^(2)z^(4)-24w^(2)z^(2)))/(18w^(4)z^(2))

22. Which expression below simplifies to 2(z2−2)3w2 \frac{2\left(z^{2}-2\right)}{3 w^{2}} ?\newlineA. (4w2z4−16w2z2)9w6z4 \frac{\left(4 w^{2} z^{4}-16 w^{2} z^{2}\right)}{9 w^{6} z^{4}} \newlineB. (4w2z4−16w2z2)9w4z2 \frac{\left(4 w^{2} z^{4}-16 w^{2} z^{2}\right)}{9 w^{4} z^{2}} \newlineC. (12w2z4−24w2z2)18w6z4 \frac{\left(12 w^{2} z^{4}-24 w^{2} z^{2}\right)}{18 w^{6} z^{4}} \newline(D. (12w2z4−24w2z2)18w4z2 \frac{\left(12 w^{2} z^{4}-24 w^{2} z^{2}\right)}{18 w^{4} z^{2}}

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Full solution

Q. 22. Which expression below simplifies to 2(z2−2)3w2 \frac{2\left(z^{2}-2\right)}{3 w^{2}} ?\newlineA. (4w2z4−16w2z2)9w6z4 \frac{\left(4 w^{2} z^{4}-16 w^{2} z^{2}\right)}{9 w^{6} z^{4}} \newlineB. (4w2z4−16w2z2)9w4z2 \frac{\left(4 w^{2} z^{4}-16 w^{2} z^{2}\right)}{9 w^{4} z^{2}} \newlineC. (12w2z4−24w2z2)18w6z4 \frac{\left(12 w^{2} z^{4}-24 w^{2} z^{2}\right)}{18 w^{6} z^{4}} \newline(D. (12w2z4−24w2z2)18w4z2 \frac{\left(12 w^{2} z^{4}-24 w^{2} z^{2}\right)}{18 w^{4} z^{2}}
  1. Simplify Option A: Let's start by simplifying each option to see if it matches the given expression (2(z2−2))/(3w2)(2(z^{2}-2))/(3w^{2}).\newlineOption A: ((4w2z4−16w2z2))/(9w6z4)((4w^{2}z^{4}-16w^{2}z^{2}))/(9w^{6}z^{4})\newlineWe can factor out 4w2z24w^2z^2 from the numerator and cancel out w2z4w^2z^4 from the numerator and denominator.\newlineSimplification: (4w2z2(z2−4))/(9w6z4)=(4/9)(z2−4)/(w4)(4w^2z^2(z^2-4))/(9w^6z^4) = (4/9)(z^2-4)/(w^4)\newlineThis does not match the given expression because the powers of ww and zz do not match.
  2. Simplify Option B: Option B: (4w2z4−16w2z2)9w4z2\frac{(4w^{2}z^{4}-16w^{2}z^{2})}{9w^{4}z^{2}}\newlineWe can factor out 4w2z24w^2z^2 from the numerator and cancel out w2z2w^2z^2 from the numerator and denominator.\newlineSimplification: (4w2z2(z2−4))9w4z2=49(z2−4)w2\frac{(4w^2z^2(z^2-4))}{9w^4z^2} = \frac{4}{9}\frac{(z^2-4)}{w^2}\newlineThis does not match the given expression because the coefficient in front of the simplified expression is 49\frac{4}{9} instead of 23\frac{2}{3}.
  3. Simplify Option C: Option C: (12w2z4−24w2z2)18w6z4\frac{(12w^{2}z^{4}-24w^{2}z^{2})}{18w^{6}z^{4}}\newlineWe can factor out 12w2z212w^2z^2 from the numerator and cancel out w2z4w^2z^4 from the numerator and denominator.\newlineSimplification: (12w2z2(z2−2))18w6z4=1218(z2−2)w4\frac{(12w^2z^2(z^2-2))}{18w^6z^4} = \frac{12}{18}\frac{(z^2-2)}{w^4}\newlineThis does not match the given expression because the powers of ww do not match and the coefficient in front of the simplified expression is 1218\frac{12}{18} instead of 23\frac{2}{3}.
  4. Simplify Option D: Option D: (12w2z4−24w2z2)18w4z2\frac{(12w^{2}z^{4}-24w^{2}z^{2})}{18w^{4}z^{2}}\newlineWe can factor out 12w2z212w^2z^2 from the numerator and cancel out w2z2w^2z^2 from the numerator and denominator.\newlineSimplification: (12w2z2(z2−2))18w4z2=(12/18)(z2−2)w2\frac{(12w^2z^2(z^2-2))}{18w^4z^2} = \frac{(12/18)(z^2-2)}{w^2}\newlineSimplify the coefficient: (12/18)(12/18) simplifies to (2/3)(2/3).\newlineSo, the simplified expression is (2/3)(z2−2)w2\frac{(2/3)(z^2-2)}{w^2}, which matches the given expression 2(z2−2)3w2\frac{2(z^{2}-2)}{3w^{2}}.

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