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

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