1.
(y - 2)(y - 4)
Multiply all terms on the right with y, then do the same with -2
Multiply y by y:
[tex]y^2[/tex]
Then y by -4:
[tex]y^2-4y[/tex]
Then -2 by y:
[tex]y^2-4y-2y[/tex]
Then -2 by -4:
[tex]y^2-4y-2y+8 = y^2-6y + 8\\[/tex]
We already have [tex]y^2[/tex] first, then [tex]y[/tex] and finally [tex]y^0[/tex], so we don't have to rearrange anything.
Answer: [tex]y^2-6y+8[/tex]
2.
[tex](6y^2)(-8x^3-y+5)[/tex]
Multiply all terms on the right with 6y^2:
[tex]6y^2 * -8x^3 + 6y^2 * -y + 6y^2 * 5\\-48x^3y^2 - 6y^3 + 30y^2[/tex]
Not sure which order is preferred here, you can put either the [tex]y^3[/tex] term first or [tex]x^3y^2[/tex].
Answer: [tex]-6y^3 - 48x^3y^3 + 30y^2[/tex]
3.
[tex]2x^4(8x^5-7x+10)[/tex]
Multiply all terms in the right parenthesis with 2x^4 :
[tex]2x^4 * 8x^5 + 2x^4 * -7x + 2x^4 * 10\\16x^9 -14x^5 + 20x^4[/tex]
Answer: [tex]16x^9 -14x^5 + 20x^4[/tex]
4.
[tex](7x+3)(2x-4)[/tex]
First, multiply all terms on the right with 7x. Then do the same with 3.
[tex]7x * 2x + 7x*-4 + 3*2x + 3*-4\\14x^2 - 28x + 6x -12\\14x^2 - 22x - 12[/tex]
Answer: [tex]14x^2-22x-12[/tex]
5.
[tex](3x+4y)^2[/tex]
[tex](3x+4y)(3x+4y)[/tex]
Multiply all terms on the right with 3x, then do the same with 4y:
[tex]3x*3x + 3x*4y + 4y*3x + 4y*4y\\9x^2 + 12xy + 12xy + 16y^2\\9x^2 + 24xy + 16y^2[/tex]
Here, I choose to rearrange them to x^2, then y^2, then xy:
Answer: [tex]9x^2+16y^2 + 24xy[/tex]
6.
[tex]-5x^6(x^3+xy-2y^2)[/tex]
Like previous similar ones, we multiply all terms in the parenthesis with -5x^6:
[tex]-5x^6 * x^3 -5x^6 * xy -5x^2*-2y^2\\-5x^9 - 5x^7y +10x^2y^2[/tex]
Answer: [tex]-5x^9 - 5x^7y +10x^2y^2[/tex]
7.
[tex](-x^2y)(5x^3+4x^2y+5y^4)[/tex]
Multiply all terms in the right parenthesis with -x^2y:
[tex]-x^2y*5x^3 -x^2y*4x^2y -x^2y*5y^4\\-5x^5y - 4x^4y^2 - 5x^2y^5[/tex]
Here, you can also choose which order you believe is appropriate.
Answer: [tex]-5x^5y - 4x^4y^2 - 5x^2y^5[/tex]
8.
[tex](7x-3y)(-2x+5y)[/tex]
Multiply the terms on the right with 7x, then with -3y:
[tex]7x*-2x + 7x*5y -3y*-2x-3y*5y\\-14x^2 + 35xy +6xy - 15y^2\\-14x^2 + 41xy - 15y^2[/tex]
Answer: [tex]-14x^2 + 41xy - 15y^2[/tex]
