Question

Умножение многочлен на одночлен 1. (8+3x) (2y-1)=? 2. (2a-1) (3a+7)=? 3. (3a-2b) (2a-3b)=? 4. (15a+27) (-5a-9)=?

Answer 1

Ответ:

Пошаговое объяснение:

1. (8+3x) (2y-1)=16у-8+6ху-3х

2. (2a-1) (3a+7)==6а²+14а-3а-7=6а²+11-7

3. (3a-2b) (2a-3b)==6а²-9аб-4аб+6б²=6а²-13аб+6б²

4. (15a+27) (-5a-9)=-75а²-135а-135а-243=-75а²-270а-243

Answer 2

To multiply a polynomial by a monomial, you need to distribute the monomial term to every term in the polynomial and then simplify the result. Let's perform the multiplication for each given expression:

1. (8+3x)(2y-1):

Apply the distributive property: (8+3x)(2y-1) = 8 * 2y + 8 * (-1) + 3x * 2y + 3x * (-1)

Simplify: 16y - 8 + 6xy - 3x

The result is 16y + 6xy - 3x - 8.

2. (2a-1)(3a+7):

Apply the distributive property: (2a-1)(3a+7) = 2a * 3a + 2a * 7 - 1 * 3a - 1 * 7

Simplify: 6a^2 + 14a - 3a - 7

Combine like terms: 6a^2 + 11a - 7

The result is 6a^2 + 11a - 7.

3. (3a-2b)(2a-3b):

Apply the distributive property: (3a-2b)(2a-3b) = 3a * 2a + 3a * (-3b) - 2b * 2a - 2b * (-3b)

Simplify: 6a^2 - 9ab - 4ab + 6b^2

Combine like terms: 6a^2 - 13ab + 6b^2

The result is 6a^2 - 13ab + 6b^2.

4. (15a+27)(-5a-9):

Apply the distributive property: (15a+27)(-5a-9) = 15a * (-5a) + 15a * (-9) + 27 * (-5a) + 27 * (-9)

Simplify: -75a^2 - 135a - 135a - 243

Combine like terms: -75a^2 - 270a - 243

The result is -75a^2 - 270a - 243.

So, the simplified expressions for the given multiplications are:

1. 16y + 6xy - 3x - 8
2. 6a^2 + 11a - 7
3. 6a^2 - 13ab + 6b^2
4. -75a^2 - 270a - 243.