Question

Выполните умножение1)(3x-1)(2x+5);2)(4x-y)(2x-3y);3)(m+3n)(m^2-6mn-n^2);4)x(3x-1)(2x+5).помогите пожалуйста

Answer 1

1)5x+15-2x-5
2)8x-(4x×3y)-2xy-3y^2
3)m^3-6m^2n-n^2m+3nm^2-(3n×6mn)-3n^3
4)(3x^2-x)(2x+5)
6x^3+(5×3x^2)-2x^2-5x

Answer 2

Умножение выражений

1) (3x-1)(2x+5):

To multiply these two expressions, we can use the distributive property. We multiply each term in the first expression by each term in the second expression and then combine like terms.

The first expression is (3x-1) and the second expression is (2x+5).

Multiplying the first term of the first expression (3x) by each term in the second expression (2x and 5) gives us: 3x * 2x = 6x^2 3x * 5 = 15x

Multiplying the second term of the first expression (-1) by each term in the second expression (2x and 5) gives us: -1 * 2x = -2x -1 * 5 = -5

Now, we can combine the like terms: 6x^2 + 15x - 2x - 5

Simplifying further, we get the final result: 6x^2 + 13x - 5

2) (4x-y)(2x-3y):

Using the distributive property, we multiply each term in the first expression by each term in the second expression and then combine like terms.

The first expression is (4x-y) and the second expression is (2x-3y).

Multiplying the first term of the first expression (4x) by each term in the second expression (2x and -3y) gives us: 4x * 2x = 8x^2 4x * -3y = -12xy

Multiplying the second term of the first expression (-y) by each term in the second expression (2x and -3y) gives us: -y * 2x = -2xy -y * -3y = 3y^2

Now, we can combine the like terms: 8x^2 - 12xy - 2xy + 3y^2

Simplifying further, we get the final result: 8x^2 - 14xy + 3y^2

3) (m+3n)(m^2-6mn-n^2):

Using the distributive property, we multiply each term in the first expression by each term in the second expression and then combine like terms.

The first expression is (m+3n) and the second expression is (m^2-6mn-n^2).

Multiplying the first term of the first expression (m) by each term in the second expression (m^2, -6mn, and -n^2) gives us: m * m^2 = m^3 m * -6mn = -6m^2n m * -n^2 = -mn^2

Multiplying the second term of the first expression (3n) by each term in the second expression (m^2, -6mn, and -n^2) gives us: 3n * m^2 = 3m^2n 3n * -6mn = -18mn^2 3n * -n^2 = -3n^3

Now, we can combine the like terms: m^3 - 6m^2n - mn^2 + 3m^2n - 18mn^2 - 3n^3

Simplifying further, we get the final result: m^3 - 3m^2n - 19mn^2 - 3n^3

4) x(3x-1)(2x+5):

To multiply these expressions, we can use the distributive property. We multiply each term in the second expression by the first expression, and then multiply the result by x.

The first expression is x, the second expression is (3x-1), and the third expression is (2x+5).

Multiplying the second expression (3x-1) by the third expression (2x+5) gives us: (3x * 2x) + (3x * 5) + (-1 * 2x) + (-1 * 5) = 6x^2 + 15x - 2x - 5

Now, we multiply the result by x: x * (6x^2 + 15x - 2x - 5) = 6x^3 + 15x^2 - 2x^2 - 5x

Simplifying further, we get the final result: 6x^3 + 13x^2 - 5x