Q. Multiply. Write your answer in simplest form.u25u−4×(u−4)
Rewrite Expression: Rewrite the given expression for clarity.The given expression is 5u−u24∗(u−4).We can rewrite this as u25u−4∗1u−4 to make it clear that we are multiplying two fractions.
Multiply Numerators and Denominators: Multiply the numerators and the denominators.When multiplying fractions, we multiply the numerators together and the denominators together.So, (5u−4)/u2×(u−4)/1 becomes (5u−4)×(u−4)/(u2×1).
Simplify Numerator by Multiplying Binomials: Simplify the numerator by multiplying the binomials.We use the distributive property (FOIL) to multiply the binomials (5u−4) and (u−4).This gives us 5u×u+5u×(−4)−4×u−4×(−4).Calculating each term, we get 5u2−20u−4u+16.Combining like terms, we get 5u2−24u+16.
Simplify Denominator: Simplify the denominator.Since the denominator is just u2×1, it simplifies to u2.
Write Simplified Expression: Write the simplified expression.The simplified expression is (5u2−24u+16)/u2.
Check Further Simplification: Check if further simplification is possible.We 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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