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Friday 23rd of March
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 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Multiplying Special Polynomials

## Examples

Use the methods for multiplying binomials to multiply and simplify the following.

1.Multiply and Simplify:

(3x + 5)(3x - 5) - (2x + 3)(2x - 3) Note that these are conjugates. Watch signs. 9

x2 - 25 - (4x2 - 9) Remove parentheses carefully:

9x2 - 25 - 4x2 + 9 5x2 - 16

2. (3x + 5)2 - (2x + 3)2 Square the binomials and simplify. Watch signs.

9x2 + 30x + 25 - (4x2 + 12x + 9) Remove parentheses carefully:

9x2 + 30x + 25 - 4x2 - 12x - 9 5x2 + 18x + 16

3. (2x + 3)3 Use the pattern in the example above then multiply a binomial times polynomial

(2x + 3)3 = 8x3 + 36x2 + 54x + 27

## Applications

1. Number Problem: Use the difference of squares to multiply 93 Ã— 87 .

93 = 90 + 3 and 87 = 90 â€“ 3

93 Ã— 87 = (90 + 3)( 90 â€“ 3) = 902 â€“ 32

902 â€“ 32 = 8100 - 9 = 8091

Check:

2. Number Problem: Write an expression for the sum of the squares of three consecutive odd (or even) numbers. Then simplify the expression.

Let x be the first number, then x + 2 and x + 4 are the next two.

If x is odd all are odd and if x is even all are even:

N = x2 + (x + 2)2 + (x + 4)2

N = x2 + (x2 + 4x + 4) + (x2 + 8x + 16)

N = 3x2 + 12x + 20

Check:

Odd: x = 3

32 + 52 + 72 = 9 + 25 + 49 = 83 or 3(3)2 + 12(3) + 20 = 83

Even: x = 2

22 + 42 + 62 = 4 + 16 + 36 = 56 or 3(2)2 + 12(2) + 20 = 56