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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