Foil Methods

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FOIL : F means first, O means outside, I means inside and l means last.

First multiply the first variable in each binomial.
Multiply outside variable.
Multiply the inside variables.
Multiply last variable in each binomial.

The parentheses are used for the multiplication sign. This method is used to multiply two.

Example : Let us find the multiplication of the following binomials

(a + b) (a²- ab + b²)

Solution : The given problem is (a + b) (a²- ab + b²)

Apply the foil method to multiply the polynomials.

(a + b) (a²- ab + b²) = a3 – a² b + ab² + ba² – b ab + b. b

= a3 – a² b + ab² + ba² – b ab + b. b = a3 – a² b + ab² + ba² – ab² + b²

Hence the multiplication of (a + b) (a²- ab + b²) is a3 – a² b + ab² + ba² – ab² + b²

Example : Let us find the multiplication of the following binomials

(x + y + z) (X² + y² + z ²+ xy + yz + zx)

Solution : The given problem is

(x + y + z) (X² + y² + z ²+ xy + yz + zx)

The multiplication of the two binomials is given below

(x + y + z) (x² + y² + z ²+ xy + yz + zx)  = (x³ + xy² + xz² + xxy + xyz + x zx + yx² + y³ + yz² + yxy + y.yz + xyz + zx² + zy² + z³ + xyz + zyz + z.zx)

= (x³ + xy² + xz² + x²y + xyz + x²z + yx² + y³ + yz² + xy² + y²z + xyz + zx² + zy² + z³ + xyz + yz² + z²x)

= (x³ + y³ + z³ + xy² + xz² + x²y + 3xyz + x²z + yx² + yz² + xy² + y²z + zx² + zy² + yz² + z²x)