Prentice Hall Algebra 1

Chapter 8 Polynomials and Factoring > 8-4 Multiplying Special Cases > Practice and Problem-Solving Exercises

You can use the rule for the product of a sum and difference to calculate products using mental math.

Problem 5 Using Mental Math

GRIDDED RESPONSE

What is 64 middle dot 56 question mark

Think

How can you write 64 middle dot 56 as the product of a sum and difference?

Find the number halfway between the factors. 60 is 4 units from each factor. Write the factors in terms of 60 and 4.

An answer sheet shows the circles for 3584 filled in.

64 ⋅ 56 = ( 60 + 4 ) ( 60 − 4 ) Write as a product of a sum and a difference . = 60 2 − 4 2 Use ( a + b ) ( a − b ) = a 2 − b 2 . = 3600 − 16 Simplify powers . = 3584 Simplify . table with 4 rows and 4 columns , row1 column 1 , 64 dot 56 , column 2 equals , column 3 open 60 plus 4 close open 60 minus 4 close , column 4 cap writeasaproductofasumandadifference . . , row2 column 1 , , column 2 equals , column 3 60 squared , minus , 4 squared , column 4 cap use , open eh plus b close open eh minus b close equals , eh squared , minus , b squared , . , row3 column 1 , , column 2 equals , column 3 3600 , minus 16 , column 4 cap simplifypowers . . , row4 column 1 , , column 2 equals , column 3 3584 , column 4 cap simplify , . , end table

✓ Got It?

What is 52 middle dot 48 question mark Use mental math.

✓ Lesson Check

Do you know HOW?

Simplify each product.

( c + 3 ) ( c + 3 ) open c plus 3 close open c plus 3 close
( g − 4 ) 2 open g minus 4 close squared
( 2 r − 3 ) ( 2 r + 3 ) open 2 r minus 3 close open 2 r plus 3 close
A square has side length (2x + 3) in. What is the area of the square?

Do you UNDERSTAND?

What rule would you use to find each product? Why?

( 3 x − 1 ) 2 open 3 x minus 1 close squared
( 4 x − 9 ) ( 4 x + 9 ) open 4 x minus 9 close open 4 x plus 9 close
( 7 x + 2 ) ( 7 x + 2 ) open 7 x plus 2 close open 7 x plus 2 close
Reasoning How do you know whether it is convenient to use the rule for the product of a sum and difference to mentally multiply two numbers?

Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Simplify each expression.

( w + 5 ) 2 open w plus 5 close squared
( h + 2 ) 2 open h plus 2 close squared
( 3 s + 9 ) 2 open 3 s plus 9 close squared
( 2 n + 7 ) 2 open 2 n plus 7 close squared
( a − 8 ) 2 open eh minus 8 close squared
( k − 11 ) 2 open k minus 11 close squared
( 5 m − 2 ) 2 open 5 m minus 2 close squared
( 4 x − 6 ) 2 open 4 x minus 6 close squared

See Problem 2.

Geometry The figures below are squares. Find an expression for the area of each shaded region. Write your answers in standard form.

End ofPage 495