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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