Special Products of Polynomials
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Transcript of Special Products of Polynomials
March 24, 2014Pages 569-571
Find the product.
1. (3x + 4)2
= 9x2 + 24x + 16 Simplify.
2. (5x – 2y)2
=25x2 – 20xy + 4y2 Simplify.
= (3x + 4)(3x + 4)
= (5x – 2y)(5x - 2y)
= 9x2 + 12x + 12x + 16
= 25x2 – 10xy – 10xy + 4y2
3. (x + 3)2
= x2 + 6x + 9 Simplify.
4. (2x + 1)2
= 4x2 + 4x + 1 Simplify.
= (x + 3)(x + 3)
= (2x + 1) + (2x + 1)
= x2 + 3x + 3x + 9
= 4x2 + 2x + 2x + 1
5. (4x – y)2
= 16x2 – 8xy + y2 Simplify.
= (4x – y)(4x – y)
= 16x2 – 4xy – 4xy + y2
Use special products to find the product 26 34.
SOLUTION
Notice that 26 is 4 less than 30 while 34 is 4 more than 30.
26 34 Write as product of difference and sum.
= 302 – 42 Sum and difference pattern
= 900 – 16 Evaluate powers.
= 884 Simplify.
= (30 – 4)(30 + 4)
REVIEW
6. (t + 5)(t – 5) Sum and difference pattern
= t2 – 25 Simplify.
7. (3x + y)(3x – y) Sum and difference pattern
= 9x2 – y2 Simplify.
= t2 – 52
= (3x)2 – y2
Page 572, #4-34, even