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Multiply. Write your answer in simplest form.\newline5u4u2×(u4)\frac{5u - 4}{u^2} \times (u - 4)

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Q. Multiply. Write your answer in simplest form.\newline5u4u2×(u4)\frac{5u - 4}{u^2} \times (u - 4)
  1. Rewrite Expression: Rewrite the given expression for clarity.\newlineThe given expression is 5u4u2(u4)5u - \frac{4}{u^2} * (u - 4).\newlineWe can rewrite this as 5u4u2u41\frac{5u - 4}{u^2} * \frac{u - 4}{1} to make it clear that we are multiplying two fractions.
  2. Multiply Numerators and Denominators: Multiply the numerators and the denominators.\newlineWhen multiplying fractions, we multiply the numerators together and the denominators together.\newlineSo, (5u4)/u2×(u4)/1(5u - 4)/u^2 \times (u - 4)/1 becomes (5u4)×(u4)/(u2×1)(5u - 4) \times (u - 4) / (u^2 \times 1).
  3. Simplify Numerator by Multiplying Binomials: Simplify the numerator by multiplying the binomials.\newlineWe use the distributive property (FOIL) to multiply the binomials (5u4)(5u - 4) and (u4)(u - 4).\newlineThis gives us 5u×u+5u×(4)4×u4×(4)5u \times u + 5u \times (-4) - 4 \times u - 4 \times (-4).\newlineCalculating each term, we get 5u220u4u+165u^2 - 20u - 4u + 16.\newlineCombining like terms, we get 5u224u+165u^2 - 24u + 16.
  4. Simplify Denominator: Simplify the denominator.\newlineSince the denominator is just u2×1u^2 \times 1, it simplifies to u2u^2.
  5. Write Simplified Expression: Write the simplified expression.\newlineThe simplified expression is (5u224u+16)/u2(5u^2 - 24u + 16) / u^2.
  6. Check Further Simplification: Check if further simplification is possible.\newlineWe look for common factors in the numerator and the denominator. In this case, there are no common factors, so the expression is already in its simplest form.

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