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Grade 7 - Mathematics
4.26 Multiplication of Two Binomials (Geometrical Proof)

Multiplication of two binomials

Suppose AB = a units, BC = b units, Ag = c units, GF = d units
Therefore GH = a units, HI = b units, BH = C units, HE = d units
Therefore AF = AB + BC = (a + b) units
AF = AG + GF = (c + d) units
Area of rectangle ACDF = AC * AF
= (a + b) (c + d) Sq. units    ..........I
But area of rectangle ACDF
= Area of rectangle ABHG + Area of rectangle BCIH + Area of rectangle IDEH + Area of rectangle GHEF
= AB * AG + BC * BH + GH * GF + HI * HE
= (a.c + b.c + a.d + b.d) Sq. units    ..........II
Result I and II gives the area of the same rectangle ACDF
from I and II
Ž(a + b) (c + d) = (a.c + b.c + a.d + b.d)


Directions: Solve the following problems. Also write at least ten examples of your own.
Q 1: (6x+5)(4y+7) = _____?
Answer:

Q 2: (7x+10)(5y+9) = _____?
Answer:

Q 3: (3x+7)(2y+3) = _____?
Answer:

Q 4: (4x+6)(7y+9) = _____?
Answer:

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