Problem 5 Factoring Out a Common Factor

What is the factored form of 24 g 2 − 6 ? 24 g squared , minus 6 question mark

24 g 2 − 6 = 6 ( 4 g 2 − 1 ) Factor out the GCF, 6.   = 6 [ ( 2 g ) 2 − 1 2 ] Write the difference as  a 2 − b 2 .   = 6 ( 2 g + 1 ) ( 2 g − 1 ) Use the rule for the difference of squares. table with 3 rows and 4 columns , row1 column 1 , 24 g squared , minus 6 , column 2 equals , column 3 6 open , 4 g squared , minus 1 close , column 4 cap factor out the cap gcap ccap fcomma 6. , row2 column 1 , , column 2 equals , column 3 6 left bracket . open , 2 g , close squared . minus , 1 squared , right bracket , column 4 cap write the difference as . eh squared , minus , b squared , . , row3 column 1 , , column 2 equals , column 3 6 open 2 g plus 1 close open 2 g minus 1 close , column 4 cap use the rule for the difference of squares. , end table

✓ Got It?

5. What is the factored form of each expression?

   1. 12 t 2 − 48 12 t squared , minus 48
   2. 12 x 2 + 12 x + 3 12 x squared , plus 12 x plus 3

Think

Is 24 g 2 − 6 24 g squared , minus 6  a difference of two squares?

No. 24 g 2 24 g squared  and 6 are not perfect squares. To get a difference of squares, you must first factor out the GCF.

✓ Lesson Check

Do you know HOW?

Factor each expression.

1. y 2 − 16 y + 64 y squared , minus 16 y plus 64
2. 9 q 2 + 12 q + 4 9 q squared , plus 12 q plus 4
3. p 2 − 36 p squared , minus 36
4. The area of a square is 36 w 2 + 60 w + 25 . 36 w squared , plus 60 w plus 25 .  What is the side length of the square?

Do you UNDERSTAND?

Identify the rule you would use to factor each expression.

5. 81 r 2 − 90 r + 25 81 r squared , minus 90 r plus 25
6. k 2 + 12 k + 36 k squared , plus 12 k plus 36
7. 9 h 2 − 64 9 h squared , minus 64
8. Reasoning Explain how to determine whether a binomial is a difference of two squares.