Question

Multiply the following vertically(3x+2y+1) (2x-3y-5)

Answer 1

To multiply the expressions (3x+2y+1) and (2x-3y-5) vertically, you can use the distributive property and follow these steps:

1. Start by multiplying the first term in the first expression, 3x, by each term in the second expression:

- (3x) * (2x) = 6x^2

- (3x) * (-3y) = -9xy

- (3x) * (-5) = -15x

2. Move on to the second term in the first expression, 2y:

- (2y) * (2x) = 4xy

- (2y) * (-3y) = -6y^2

- (2y) * (-5) = -10y

3. Finally, multiply the last term in the first expression, 1, by each term in the second expression:

- (1) * (2x) = 2x

- (1) * (-3y) = -3y

- (1) * (-5) = -5

Now, let's combine the like terms:

6x^2 + (-9xy) + (-15x) + 4xy + (-6y^2) + (-10y) + 2x + (-3y) + (-5)

Simplifying this expression further, we have:

6x^2 - 5x - 9xy + 4xy - 6y^2 - 10y + 2x - 3y - 5

Therefore, the result of multiplying (3x+2y+1) and (2x-3y-5) vertically is 6x^2 - 5x - 9xy + 4xy - 6y^2 - 10y + 2x - 3y - 5.

Explanation:

Answer 2

To multiply the expressions (3x + 2y + 1) and (2x - 3y - 5) vertically, we will use the distributive property and multiply each term from the first expression with each term from the second expression.

Starting with the first term in the first expression, which is 3x, we multiply it with each term in the second expression:

(3x) * (2x) = 6x^2

(3x) * (-3y) = -9xy

(3x) * (-5) = -15x

Next, we move to the second term in the first expression, which is 2y:

(2y) * (2x) = 4xy

(2y) * (-3y) = -6y^2

(2y) * (-5) = -10y

Finally, we multiply the last term in the first expression, which is 1, with each term in the second expression:

(1) * (2x) = 2x

(1) * (-3y) = -3y

(1) * (-5) = -5

Now, let's add up all the results:

6x^2 - 9xy - 15x + 4xy - 6y^2 - 10y + 2x - 3y - 5

Simplifying this expression further, we have:

6x^2 - 5x - 6y^2 - 7xy - 13y - 5