Factor by grouping

[Jenifer]

When following the example in the book, my answer does not match the answer choices and I wanted to see what I am doing wrong. According to the example I am following ax+7x+ay+7y would be a(x+7)+y(a+7) but that is not one of the answer choices so I need to know what I am doing wrong here. How about if 7 were the greatest common factor then 7+a(x+y) Is this correct? Solve the equation for the indicated. y²-ay+8by-8ab+0for y 8 greatest common factor =is it y=-8b,y=a or y=8b, y=a I also want to ask about solving these equations x²-7x=0 so is it x=0, x=7 or x=0,x=^-7 both a positive 7 and a negative 7 seem to fit this equation, but I can only pick one and I need help with this one x-2x²=0

 

[MarkFL]

1.) Given:

$\displaystyle ax+7x+ay+7y$

we have 2 sensible choices for grouping. We could choose to group terms having a and 7 as common factors, or we could choose to group terms having x and y as common factors:

i) $\displaystyle ax+7x+ay+7y=(ax+ay)+(7x+7y)=a(x+y)+7(x+y)=(a+7)(x+y)$

ii) $\displaystyle ax+7x+ay+7y=(ax+7x)+(ay+7y)=x(a+7)+y(a+7)=(x+y)(a+7)$

2.) I assume you mean:

$\displaystyle y^2-ay+8by-8ab=0$

i) $\displaystyle y^2-ay+8by-8ab=(y^2-ay)+(8by-8ab)=y(y-a)+8b(y-a)=(y+8b)(y-a)=0$

ii) $\displaystyle y^2-ay+8by-8ab=(y^2+8by)-(ay+8ab)=y(y+8b)-a(y+8b)=(y-a)(y+8b)=0$

Now, using the zero-factor property, what are the two roots for y?

3.) What do both terms have as a common factor?

4.) Ditto.