Respuesta :
Answer:
Match each trinomial to its factored form:
1. [tex](y-2)(3y+4)[/tex]
Multiplying each term in the first expression by each term in a second expression.
[tex]y(3y+4) -2(3y+4)[/tex]
Using distributive property: [tex]a\cdot (b+c) = a\cdot b+ a\cdot c[/tex]
[tex](3y^2 + 4y) -(6y + 8)[/tex]
Remove the parenthesis, we have;
[tex]3y^2 + 4y -6y -8[/tex]
combine like term ;
[tex]3y^2-2y -8[/tex]
2. [tex](y+2)(3y-4)[/tex]
Multiplying each term in the first expression by each term in a second expression.
[tex]y(3y-4) +2(3y-4)[/tex]
Using distributive property: [tex]a\cdot (b+c) = a\cdot b+ a\cdot c[/tex]
[tex](3y^2 - 4y) + (6y - 8)[/tex]
Remove the parenthesis, we have;
[tex]3y^2 - 4y + 6y - 8[/tex]
combine like term ;
[tex]3y^2 + 2y -8[/tex]
3. [tex](3y+2)(y-5)[/tex]
Multiplying each term in the first expression by each term in a second expression.
[tex]3y(y-5) +2(y-5)[/tex]
Using distributive property: [tex]a\cdot (b+c) = a\cdot b+ a\cdot c[/tex]
[tex](3y^2 - 15y) + (2y - 10)[/tex]
Remove the parenthesis, we have;
[tex]3y^2 - 15y + 2y - 10[/tex]
combine like term ;
[tex]3y^2 -13y -10[/tex]
4. [tex](3y-2)(y+5)[/tex]
Multiplying each term in the first expression by each term in a second expression.
[tex]3y(y+5) -2(y+5)[/tex]
Using distributive property: [tex]a\cdot (b+c) = a\cdot b+ a\cdot c[/tex]
[tex](3y^2 + 15y) - (2y + 10)[/tex]
Remove the parenthesis, we have;
[tex]3y^2+ 15y - 2y - 10[/tex]
combine like term ;
[tex]3y^2 + 13y -10[/tex]
Column 1 Column 2
[tex](y-2)(3y+4)[/tex] [tex]3y^2-2y -8[/tex]
[tex](y+2)(3y-4)[/tex] [tex]3y^2+ 2y -8[/tex]
[tex](3y+2)(y-5)[/tex] [tex]3y^2 -13y -10[/tex]
[tex](3y-2)(y+5)[/tex] [tex]3y^2 + 13y -10[/tex]
Answer:
[tex]3y^2 + 2y - 8=(3y-4)(y+2)[/tex]
[tex]3y^2 + 13y - 10=(3y-2)(y+5)[/tex]
[tex]3y^2 - 13y - 10=(3y+2)(y-5)[/tex]
[tex]3y^2 - 2y - 8=(3y+4)(y-2)[/tex]
Step-by-step explanation:
Given trinomial are
[tex]3y^2 + 2y - 8\\3y^2 + 13y - 10\\3y^2 - 13y - 10\\3y^2 - 2y - 8[/tex].
we have to convert these in factored form
[tex]3y^2 + 2y - 8=3y^2+6y-4y-8[/tex]
= [tex]3y(y+2)-4(y+2)[/tex]
= [tex](3y-4)(y+2)[/tex]
[tex]3y^2 + 13y - 10=3y^2+15y-2y-10[/tex]
= [tex]3y(y+5)-2(y+5)[/tex]
= [tex](3y-2)(y+5)[/tex]
[tex]3y^2 - 13y - 10=3y^2-15y+2y-10[/tex]
= [tex]3y(y-5)+2(y-5)[/tex]
= [tex](3y+2)(y-5)[/tex]
[tex]3y^2 - 2y - 8=3y^2-6y+4y-8[/tex]
= [tex]3y(y-2)+4(y-2)[/tex]
= [tex](3y+4)(y-2)[/tex]
