Respuesta :
Answer:
1. y^2 - y - 2 = (y + 1)(y - 2)
2. 3y^2 - 27 = 3(y - 3)(y + 3)
3. y^4 - 16 = (y - 2)(y + 2)(y^2 + 4)
4. y^2 - 12y + 36 = (y - 6)^2
5. -4y^2 + 8y + 32 = -4(y + 2)( y - 4)
6. 5y - 2 + 4y^2 - 4 = (4y - 3)(y + 2)
Step-by-step explanation:
1. y^2 - y - 2=(y - 2)(y + 1)→
y^2 - y - 2 = (y + 1)(y - 2)
2. 3y^2 - 27
Common factor 3:
[tex]3y^2-27=3(y^2-9)[/tex]
Using Difference of squares:
[tex]a^2-b^2=(a-b)(a+b)[/tex]
with:
[tex]a^2=y^2\\ \sqrt{a^2}=\sqrt{y^2}\\ a=y[/tex]
[tex]b^2=9\\ \sqrt{b^2}=\sqrt{9}\\ b=3[/tex]
3y^2 - 27=3(y - 3)(y + 3)
3. y^4 - 16
Using Difference of squares:
[tex]a^2-b^2=(a-b)(a+b)[/tex]
with:
[tex]a^2=y^4\\ \sqrt{a^2}=\sqrt{y^4}\\ a=y^2[/tex]
[tex]b^2=16\\ \sqrt{b^2}=\sqrt{16}\\ b=4[/tex]
y^4 - 16 = (y^2-4)(y^2+4)
Using Difference of squares in the first parentheses:
[tex]a^2-b^2=(a-b)(a+b)[/tex]
with:
[tex]a^2=y^2\\ \sqrt{a^2}=\sqrt{y^2}\\ a=y[/tex]
[tex]b^2=4\\ \sqrt{b^2}=\sqrt{4}\\ b=2[/tex]
y^4 - 16 = (y - 2)(y + 2)(y^2 + 4)
4. y^2 - 12y + 36 = (y - 6)(y - 6)
y^2 - 12y + 36 = (y - 6)^2
5. -4y^2 + 8y + 32
Common factor -4:
[tex]-4y^2+8y+32=-4(y^2-2y-8)\\ -4y^2+8y+32=-4(y-4)(y+2)[/tex]
-4y^2 - 12y + 32 = -4(y + 2)( y - 4)
6. 5y - 2 + 4y^2 - 4
Adding like terms:
5y - 2 + 4y^2 - 4 = 5y + 4y^2 - 6
Ordering the terms:
5y - 2 + 4y^2 - 4 = 4y^2 + 5y - 6
Writing 5y like: 8y - 3y = -3y + 8y
5y - 2 + 4y^2 - 4 = 4y^2 - 3y + 8y - 6
Grouping terms:
5y - 2 + 4y^2 - 4 = (4y^2 - 3y) + (8y - 6)
Common factor in the first parentheses y and 2 in the second parentheses:
5y - 2 + 4y^2 - 4 = y(4y - 3) + 2(4y - 3)
Common factor 4y-3:
5y - 2 + 4y^2 - 4 = (4y - 3)(y + 2)
