Multiplication of a Multinomial by a Monomial
Suppose AB = a units, BC = b units, CD = c units, AH = k units
Therefore AD = AB + BC + CD = (a + b + c)units
Area of rectangle ADEH = AD * AH
= (a + b + c) * k sq. units ..........I
But area of rectangle ADEH
= Area of rectangle ABGH + Area of rectangle BCFG + Area of rectangle CDEF
= (AB * AH) + (BC * CF) + (CD * DE)
= (a.k + b.k + c.k) sq. units ..........II
Results I and II give the are of the same rectangle ADEH
Therefore from I and II
(a + b + c) * k = (a.k + b.k + c.k)
Directions: Solve the following problems. Also write at least ten examples of your own.
