Question

algebra 1
worksheet: 9.4 dots
factor:

1. ( m^2 - 4 )
2. ( 5y^2 - 405 )
3. ( m^2 - 121 )
4. ( 9r^2 - 16 )
5. ( a^2 - 144 )
6. ( c^2 + 16 )
7. ( 4j^2 - 49 )
8. ( 3y^2 + 12y + 12 )
9. ( k^2 - 6k + 9 )
10. ( x^2 - 11x + 121 )
11. ( 9 + 21a + 6a^2 )
12. ( 81 - 18x + x^2 )

name:
represents the...
f ( 9 leq x leq 11 )
g ( 8 leq x leq 12 )
h ( 8 leq x leq 11 )
( x leq 12 )
in a pro...
when ( y = 5, x = 3 ), find the val...

1. what is the equation in standard form, o...

Explanation:

Step1: Factor difference of squares

$m^2 - 4 = (m-2)(m+2)$

Step2: Factor out GCF, then difference of squares

$5y^2 - 405 = 5(y^2-81) = 5(y-9)(y+9)$

Step3: Factor difference of squares

$m^2 - 121 = (m-11)(m+11)$

Step4: Factor difference of squares

$9r^2 - 16 = (3r-4)(3r+4)$

Step5: Factor difference of squares

$a^2 - 144 = (a-12)(a+12)$

Step6: Factor perfect square trinomial

$c^2 + 16 = (c+4)^2$

Step7: Factor difference of squares

$4a^2 - 49 = (2a-7)(2a+7)$

Step8: Factor out GCF, then perfect square trinomial

$3y^2 + 12y + 12 = 3(y^2+4y+4) = 3(y+2)^2$

Step9: Factor perfect square trinomial

$k^2 - 6k + 9 = (k-3)^2$

Step10: Factor perfect square trinomial

$x^2 - 11x + 121 = (x-11)^2$

Step11: Rearrange, factor perfect square trinomial

$9 + 21a + 6a^2 = 6a^2+21a+9 = 3(2a^2+7a+3) = 3(2a+1)(a+3)$

Step12: Rearrange, factor difference of squares

$81 - 18x + x^2 = x^2-18x+81 = (x-9)^2$

Answer:

1. $(m-2)(m+2)$
2. $5(y-9)(y+9)$
3. $(m-11)(m+11)$
4. $(3r-4)(3r+4)$
5. $(a-12)(a+12)$
6. $(c+4)^2$
7. $(2a-7)(2a+7)$
8. $3(y+2)^2$
9. $(k-3)^2$
10. $(x-11)^2$
11. $3(2a+1)(a+3)$
12. $(x-9)^2$