$$ \begin{array}{cl} ext { EJERCICIO28 } \ \vdots & ext { Realiza los siguientes productos: } \ \vdots & ext { 1. }\left(4 a^{2}-7 a b ight)\left(2 a^{3} b ight) \ \vdots & ext { 2. }(-3 m)\left(5 m^{4}-3 m^{3}+6 m-3 ight) \ \vdots & ext { 3. }\left(3 x^{3}-7 x^{2}-2 x ight)(x y) \ \vdots & ext { 4. }(-3 a b)\left(2 a^{2}-7 a b+8 b^{2} ight) \ \vdots & ext { 5. }\left(6 a^{3} b^{2}-7 a^{2} b^{3}+4 a b^{5} ight)\left(4 a^{5} b^{2} ight) \ \vdots & ext { 6. }\left(-5 x y^{2} z ight)\left(7 x^{6} y^{2} z-3 x^{5} y-4 x z ight) \ \vdots & ext { 7. }\left(5 m^{3} n-3 m^{4} p+6 m^{2} ight)\left(8 m p^{3} ight) \ \vdots & ext { 8. }\left(4 a^{3} c-7 a^{2} b-2 c ight)\left(-3 a c^{4} ight) \ \vdots & ext { 9. }\left(5 m^{6} n-3 m n^{4}+2 m n ight)\left(3 m^{x+1} n^{2 x} ight) \ \vdots & ext { 10. }\left(-2 x^{a-2} ight)\left(7 x^{5}-8 x^{2}+6 x^{3}-9 x+2 ight) \ \vdots & ext { 11. }\left(3 a^{2 x+1} b^{4 x}-7 a^{2 x} b^{4 x+1}-4 a^{x} b^{3 x+1} ight)\left(-3 a^{x+1} b^{1-x} ight) \ \vdots & ext { 12. }\left(-5 x^{2 m} y^{n+1} ight)\left(5 x^{3 m} y^{2 n}-2 x^{3 m+1} y^{2 n+1}-4 x^{3 m+2} y^{2 n+2} ight) \ \vdots & ext { 13. }\left(3 a^{x+2} b^{y} c^{m}-3 a^{x+1} b^{y+1} c^{2}+2 a^{x-3} b^{y-1} c ight)\left(-4 a^{3} b^{2} c^{5} ight) \ \vdots & \ \vdots & 14 .\left(\frac{1}{2} a^{2}-\frac{3}{5} b^{2}-\frac{3}{4} a b ight)\left(\frac{2}{3} a b^{2} ight) \ \vdots & \end{array} $$

Question

$$ \begin{array}{cl}	ext { EJERCICIO28 } \ \vdots & 	ext { Realiza los siguientes productos: } \ \vdots & 	ext { 1. }\left(4 a^{2}-7 a bight)\left(2 a^{3} bight) \ \vdots & 	ext { 2. }(-3 m)\left(5 m^{4}-3 m^{3}+6 m-3ight) \ \vdots & 	ext { 3. }\left(3 x^{3}-7 x^{2}-2 xight)(x y) \ \vdots & 	ext { 4. }(-3 a b)\left(2 a^{2}-7 a b+8 b^{2}ight) \ \vdots & 	ext { 5. }\left(6 a^{3} b^{2}-7 a^{2} b^{3}+4 a b^{5}ight)\left(4 a^{5} b^{2}ight) \ \vdots & 	ext { 6. }\left(-5 x y^{2} zight)\left(7 x^{6} y^{2} z-3 x^{5} y-4 x zight) \ \vdots & 	ext { 7. }\left(5 m^{3} n-3 m^{4} p+6 m^{2}ight)\left(8 m p^{3}ight) \ \vdots & 	ext { 8. }\left(4 a^{3} c-7 a^{2} b-2 cight)\left(-3 a c^{4}ight) \ \vdots & 	ext { 9. }\left(5 m^{6} n-3 m n^{4}+2 m night)\left(3 m^{x+1} n^{2 x}ight) \ \vdots & 	ext { 10. }\left(-2 x^{a-2}ight)\left(7 x^{5}-8 x^{2}+6 x^{3}-9 x+2ight) \ \vdots & 	ext { 11. }\left(3 a^{2 x+1} b^{4 x}-7 a^{2 x} b^{4 x+1}-4 a^{x} b^{3 x+1}ight)\left(-3 a^{x+1} b^{1-x}ight) \ \vdots & 	ext { 12. }\left(-5 x^{2 m} y^{n+1}ight)\left(5 x^{3 m} y^{2 n}-2 x^{3 m+1} y^{2 n+1}-4 x^{3 m+2} y^{2 n+2}ight) \ \vdots & 	ext { 13. }\left(3 a^{x+2} b^{y} c^{m}-3 a^{x+1} b^{y+1} c^{2}+2 a^{x-3} b^{y-1} cight)\left(-4 a^{3} b^{2} c^{5}ight) \ \vdots & \ \vdots & 14 .\left(\frac{1}{2} a^{2}-\frac{3}{5} b^{2}-\frac{3}{4} a bight)\left(\frac{2}{3} a b^{2}ight) \ \vdots & \end{array} $$

UpStudy AI · Accepted Answer

Vamos a realizar los productos solicitados uno por uno.

### 1. $$(4 a^{2}-7 a b)(2 a^{3} b)$$

Para realizar este producto, aplicamos la propiedad distributiva:

$$
(4 a^{2})(2 a^{3} b) + (-7 a b)(2 a^{3} b)
$$

Calculamos cada término:

1. $$4 a^{2} \cdot 2 a^{3} b = 8 a^{5} b$$
2. $$-7 a b \cdot 2 a^{3} b = -14 a^{4} b^{2}$$

Por lo tanto, el resultado es:

$$
8 a^{5} b - 14 a^{4} b^{2}
$$

### 2. $$(-3 m)(5 m^{4}-3 m^{3}+6 m-3)$$

Aplicamos la propiedad distributiva:

$$
-3 m \cdot 5 m^{4} + (-3 m)(-3 m^{3}) + (-3 m)(6 m) + (-3 m)(-3)
$$

Calculamos cada término:

1. $$-3 m \cdot 5 m^{4} = -15 m^{5}$$
2. $$-3 m \cdot -3 m^{3} = 9 m^{4}$$
3. $$-3 m \cdot 6 m = -18 m^{2}$$
4. $$-3 m \cdot -3 = 9 m$$

Por lo tanto, el resultado es:

$$
-15 m^{5} + 9 m^{4} - 18 m^{2} + 9 m
$$

### 3. $$(3 x^{3}-7 x^{2}-2 x)(x y)$$

Aplicamos la propiedad distributiva:

$$
(3 x^{3})(x y) + (-7 x^{2})(x y) + (-2 x)(x y)
$$

Calculamos cada término:

1. $$3 x^{3} \cdot x y = 3 x^{4} y$$
2. $$-7 x^{2} \cdot x y = -7 x^{3} y$$
3. $$-2 x \cdot x y = -2 x^{2} y$$

Por lo tanto, el resultado es:

$$
3 x^{4} y - 7 x^{3} y - 2 x^{2} y
$$

### 4. $$(-3 a b)(2 a^{2}-7 a b+8 b^{2})$$

Aplicamos la propiedad distributiva:

$$
(-3 a b)(2 a^{2}) + (-3 a b)(-7 a b) + (-3 a b)(8 b^{2})
$$

Calculamos cada término:

1. $$-3 a b \cdot 2 a^{2} = -6 a^{3} b$$
2. $$-3 a b \cdot -7 a b = 21 a^{2} b^{2}$$
3. $$-3 a b \cdot 8 b^{2} = -24 a b^{3}$$

Por lo tanto, el resultado es:

$$
-6 a^{3} b + 21 a^{2} b^{2} - 24 a b^{3}
$$

### 5. $$(6 a^{3} b^{2}-7 a^{2} b^{3}+4 a b^{5})(4 a^{5} b^{2})$$

Aplicamos la propiedad distributiva:

$$
(6 a^{3} b^{2})(4 a^{5} b^{2}) + (-7 a^{2} b^{3})(4 a^{5} b^{2}) + (4 a b^{5})(4 a^{5} b^{2})
$$

Calculamos cada término:

1. $$6 a^{3} b^{2} \cdot 4 a^{5} b^{2} = 24 a^{8} b^{4}$$
2. $$-7 a^{2} b^{3} \cdot 4 a^{5} b^{2} = -28 a^{7} b^{5}$$
3. $$4 a b^{5} \cdot 4 a^{5} b^{2} = 16 a^{6} b^{7}$$

Por lo tanto, el resultado es:

$$
24 a^{8} b^{4} - 28 a^{7} b^{5} + 16 a^{6} b^{7}
$$

### 6. $$(-5 x y^{2} z)(7 x^{6} y^{2} z-3 x^{5} y-4 x z)$$

Aplicamos la propiedad distributiva:

$$
(-5 x y^{2} z)(7 x^{6} y^{2} z) + (-5 x y^{2} z)(-3 x^{5} y) + (-5 x y^{2} z)(-4 x z)
$$

Calculamos cada término:

1. $$-5 x y^{2} z \cdot 7 x^{6} y^{2} z = -35 x^{7} y^{4} z^{2}$$
2. $$-5 x y^{2} z \cdot -3 x^{5} y = 15 x^{6} y^{3} z$$
3. $$-5 x y^{2} z \cdot -4 x z = 20 x^{2} y^{2} z^{2}$$

Por lo tanto, el resultado es:

$$
-35 x^{7} y^{4} z^{2} + 15 x^{6} y^{3} z + 20 x^{2} y^{2} z^{2}
$$

### 7. $$(5 m^{3} n-3 m^{4} p+6 m^{2})(8 m p^{3})$$

Aplicamos la propiedad distributiva:

$$
(5 m^{3} n)(8 m p^{3}) + (-3 m^{4} p)(8 m p^{3}) + (6 m^{2})(8 m p^{3})
$$

Calculamos cada término:

1. $$5 m^{3} n \cdot 8 m p^{3} = 40 m^{4} n p^{3}$$
2. $$-3 m^{4} p \cdot 8 m p^{3} = -24 m^{5} p^{4}$$
3. $$6 m^{2} \cdot 8 m p^{3} = 48 m^{3} p^{3}$$

Por lo tanto, el resultado es:

$$
40 m^{4} n p^{3} - 24 m^{5} p^{4} + 48 m^{3} p^{3}
$$

### 8. $$(4 a^{3
1. $$8 a^{5} b - 14 a^{4} b^{2}$$ 2. $$-15 m^{5} + 9 m^{4} - 18 m^{2} + 9 m$$ 3. $$3 x^{4} y - 7 x^{3} y - 2 x^{2} y$$ 4. $$-6 a^{3} b + 21 a^{2} b^{2} - 24 a b^{3}$$ 5. $$24 a^{8} b^{4} - 28 a^{7} b^{5} + 16 a^{6} b^{7}$$ 6. $$-35 x^{7} y^{4} z^{2} + 15 x^{6} y^{3} z + 20 x^{2} y^{2} z^{2}$$ 7. $$40 m^{4} n p^{3} - 24 m^{5} p^{4} + 48 m^{3} p^{3}$$ 8. $$-16 a^{3} c + 28 a^{2} b + 12 a c$$ 9. $$15 m^{6} n^{2} - 9 m^{2} n^{4} + 6 m n$$ 10. $$-14 x^{3} + 16 x^{2} - 12 x + 18$$ 11. $$ -9 a^{3 x+2} b^{12 x} + 21 a^{2 x} b^{12 x+1} + 12 a^{x} b^{3 x+1} $$ 12. $$-25 x^{5 m} y^{2 n+1} + 10 x^{3 m+1} y^{2 n+2} + 20 x^{3 m+2} y^{2 n+3}$$ 13. $$-12 a^{x+5} b^{y+2} c^{m+5} + 9 a^{x+4} b^{y+3} c^{2} - 8 a^{x-3} b^{y-1} c$$ 14. $$-\frac{1}{3} a^{2} b^{2} + \frac{6}{5} a b^{2} + \frac{3}{2} a^{2} b$$

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