Question

(ax + by)(cx – dy)

Answer 1

The coefficient of the xy term when  the expression is multiplied out

and the like terms  are collected is zero

Step-by-step explanation:

There two binomials we need to multiply them

The steps of multiplying two binomials

1. Multiply the first terms

2. Multiply the second terms

3. 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 terms

In (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 = zero

The coefficient of the xy term when  the expression is multiplied out

and the like terms  are collected is zero

Learn more:

you can learn more about binomials in brainly.com/question/2334388

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