MULTIPLYING ALGEBRAIC EXPRESSIONS

Example 1 :

Find the product of (5 - 2x)(3 + x).

Solution :

= (5 - 2x)(3 + x)

Using FOIL method,

= 5(3) + 5(x) - 2x(3) - 2x(x)

= 15 + 5x - 6x - 2x2

  = 15 - x - 2x2

Example 2 :

Find the product of (x + 7y)(7x - y).

Solution :

= (x + 7y)(7x - y)

Using FOIL method,

= x(7x) + x(-y) + 7y(7x) + 7y(-y)

= 7x2 - xy + 49xy - 7y2

= 7x2 + 48xy - 7y2

Example 3 :

Find the product of (a2 + b)(a + b2).

Solution :

= (a2 + b)(a + b2)

Using FOIL method,

= a2(a) + a2b2 + b(a) + b(b2)

= a3 + a2b2 + ab + b3

Example 4 :

Find the product of (a + b)(a + b2).

Solution :

= (a2 + b)(a + b2)

= a2(a) + a2b2 + b(a) + b(b2)

= a3 + a2b2 + ab + b3

Example 5 :

Find the product of (3x + 2)(4x - 3).

Solution :

= (3x + 2)(4x - 3)

Using FOIL method,

= 3x(4x) + 3x (-3) + 2(4x) + 2(-3)

= 12x2 - 9x + 8x - 6

= 12x2 - x - 6

Example 6 :

Find the product of (5 - 2x)(4 + x).

Solution :

= (5 - 2x)(4 + x)

Using FOIL method,

= 5(4) + 5 (x) - 2x(4) - 2x(x)

= 20 + 5x - 8x - 2x2

= 20 - 3x - 2x2

Example 7 :

Find the product of (3x + 2)(3x - 2).

Solution :

= (3x + 2)(3x - 2)

Using the Algebraic Identity a2 - b2 = (a + b)(a - b),

= (3x)2 - 22

= 32x2 - 22

= 9x2 - 4

Example 8 :

Find the product of (5x + 3y)(5x - 3y).

Solution :

= (5x + 3y)(5x - 3y)

Using Algebraic Identity a2 - b2 = (a + b)(a - b),

= (5x)2 - (3y)2

= 52x2 - 32y2

= 25x2 - 9y2

Example 9 :

Find the product of (x + 2)(x - 2y + 3z).

Solution :

= (x + 2)(x - 2y + 3z)

Let a = x - 2y.

= (x + 2)(a + 3z)

Using FOIL method,

= x(a) + x(3z) + 2(a) + 2(3z)

= x(a) + 3xz + 2(a) + 6z

Replace 'a' by 'x - 2y'.

= x(x - 2y) + 3xz + 2(x - 2y) + 6z

Using Distributive Property,

= x2 - 2xy + 3xz + 2x - 4y + 6z

Example 10 :

Find the product of (m + n + 1)(m + n - 1).

Solution :

(m + n + 1)(m + n - 1)

Let a = m + n.

= (a + 1)(a - 1)

Using Algebraic Identity a2 - b2 = (a + b)(a - b),

= a2 - 12

Replace 'a' by 'm + n'.

= (m + n)2 - 1

Using Algebraic Identity (a + b)2 = a2 + 2ab + b2,

= m2 + 2mn + n2 - 1

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