Question

13 points! Multiply each and write in standard form. 1-8 you do not have to give explanation but it would help. Brainiest to first answerer.

Answer 1

1.

(y - 2)(y - 4)

Multiply all terms on the right with y, then do the same with -2

Multiply y by y:

$y^2$

Then y by -4:

$y^2-4y$

Then -2 by y:

$y^2-4y-2y$

Then -2 by -4:

$y^2-4y-2y+8 = y^2-6y + 8$

We already have $y^2$ first, then $y$ and finally $y^0$, so we don't have to rearrange anything.

Answer: $y^2-6y+8$

2.

$(6y^2)(-8x^3-y+5)$

Multiply all terms on the right with 6y^2:

$6y^2 * -8x^3 + 6y^2 * -y + 6y^2 * 5\\-48x^3y^2 - 6y^3 + 30y^2$

Not sure which order is preferred here, you can put either the $y^3$ term first or $x^3y^2$.

Answer: $-6y^3 - 48x^3y^3 + 30y^2$

3.

$2x^4(8x^5-7x+10)$

Multiply all terms in the right parenthesis with 2x^4 :

$2x^4 * 8x^5 + 2x^4 * -7x + 2x^4 * 10\\16x^9 -14x^5 + 20x^4$

Answer: $16x^9 -14x^5 + 20x^4$

4.

$(7x+3)(2x-4)$

First, multiply all terms on the right with 7x. Then do the same with 3.

$7x * 2x + 7x*-4 + 3*2x + 3*-4\\14x^2 - 28x + 6x -12\\14x^2 - 22x - 12$

Answer: $14x^2-22x-12$

5.

$(3x+4y)^2$

$(3x+4y)(3x+4y)$

Multiply all terms on the right with 3x, then do the same with 4y:

$3x*3x + 3x*4y + 4y*3x + 4y*4y\\9x^2 + 12xy + 12xy + 16y^2\\9x^2 + 24xy + 16y^2$

Here, I choose to rearrange them to x^2, then y^2, then xy:

Answer: $9x^2+16y^2 + 24xy$

6.

$-5x^6(x^3+xy-2y^2)$

Like previous similar ones, we multiply all terms in the parenthesis with -5x^6:

$-5x^6 * x^3 -5x^6 * xy -5x^2*-2y^2\\-5x^9 - 5x^7y +10x^2y^2$

Answer: $-5x^9 - 5x^7y +10x^2y^2$

7.

$(-x^2y)(5x^3+4x^2y+5y^4)$

Multiply all terms in the right parenthesis with -x^2y:

$-x^2y*5x^3 -x^2y*4x^2y -x^2y*5y^4\\-5x^5y - 4x^4y^2 - 5x^2y^5$

Here, you can also choose which order you believe is appropriate.

Answer: $-5x^5y - 4x^4y^2 - 5x^2y^5$

8.

$(7x-3y)(-2x+5y)$

Multiply the terms on the right with 7x, then with -3y:

$7x*-2x + 7x*5y -3y*-2x-3y*5y\\-14x^2 + 35xy +6xy - 15y^2\\-14x^2 + 41xy - 15y^2$

Answer: $-14x^2 + 41xy - 15y^2$