MATH SOLVE

4 months ago

Q:
# (ax + by)(cx – dy)In the expression above, a, b, c, and d are non-zeroconstants and ad = bc. If ac = 18 and bd = 50, what.is the value of the coefficient of the xy term whenthe expression is multiplied out and the like termsare collected?

Accepted Solution

A:

The coefficient of the xy term when the expression is multiplied outand the like terms are collected is zeroStep-by-step explanation:There two binomials we need to multiply themThe steps of multiplying two binomials1. Multiply the first terms 2. Multiply the second terms3. Multiply the 1st tern in the first bracket by the 2nd term in the second bracket 4. Multiply the 2nd tern in the first bracket by the 1st term in the second bracket 5. Add the like termsIn (ax + by)(cx – dy) ∵ (ax)(cx) = ac x²∵ (by)(-dy) = - bd y²∵ (ax)(-dy) = - ad xy∵ (by)(cx) = bc xy- Then like terms are (- ad xy) and (bc xy) add them∵ (- ad xy) + (bc xy) = (-ad + bc) xy∴ The coefficient of the xy term is (-ad + bc)∵ ad = bc- Replace ad by bc in the bracket above∴ The coefficient of the xy term = (-bc + bc)∴ The coefficient of the xy term = zeroThe coefficient of the xy term when the expression is multiplied outand the like terms are collected is zeroLearn more:you can learn more about binomials in brainly.com/question/2334388#LearnwithBrainly