Question

Binomio al cubo
Cuatrinomio cubo perfecto
1
(x – 2y)3 =
x3


+12xy2














2
(5x + 1)3 =


+75x2


+1












3
(3a2 – 7)3 =




+441a2
-343












4
(m5n2 – m2n2)3 =
m15n6
-3m12n6
















5
( ab + b) 3=
a3b3




+b3












6
( 4c + 3 )3 =


+144c2
+108c














7
( 7 – 3y)3 =
343


+ 189y2














8
( 6a + 2b)3 =


+ 216a2b
+ 72 ab2














9
( 7 - 3a2 )3 =
343
441a2
















10
( b + ab) 3=
+b3




a3b3












11
(2y - x )3 =


-12xy2


x3












12
( 3 – 4c )3 =
27


+144c2

Answer 1

Explicación paso a paso:

Binomio al cubo:  

(a ± b)³ = a³ ± 3a²b + 3ab² ± b³

Resolvamos:

1)

(x-2y)³ = (x)³ - 3(x)²(2y) + 3(x)(2y)² - (2y)³

(x-2y)³ = x³-6x²y+12xy²-8y³

2)

(5x+1)³ = (5x)³ + 3(5x)²(1) + 3(5x)(1)² + (1)³

(5x+1)³ = 125x³+75x²+15x+1

3)

(3a²-7)³ = (3a²)³ - 3(3a²)²(7) + 3(3a²)(7)² - (7)³

(3a²-7)³ = 27a⁶-189a⁴+441a²-343

4)

(m⁵n²-m²n²)³ = (m⁵n²)³ - 3(m⁵n²)²(m²n²) + 3(m⁵n²)(m²n²)² - (m²n²)³

(m⁵-m²)³ = m¹⁵n⁶-3m¹²n⁶+3m⁹n⁶-m⁶n⁶

5)

(ab-b)³ = (ab)³ - 3(ab)²(b) + 3(ab)(b)² - (b)³

(ab-b)³ = a³b³-3a²b³+3ab³-b³

6)

(4c+3)³ = (4c)³ + 3(4c)²(3) + 3(4c)(3)² + (3)³

(4c+3)³ = 64c³+144c²+108c+27

7)

(7-3y)³ = (7)³ - 3(7)²(3y) + 3(7)(3y)² - (3y)³

(7-3y)³ = 343-441y+189y²-27y³

8)

(6a+2b)³ = (6a)³ + 3(6a)²(2b) + 3(6a)(2b)² + (2b)³

(6a+2b)³ = 216a³+216a²b+72ab²+8b³

9)

(7-3a²)³ = (7)³ - 3(7)²(3a²) + 3(7)(3a²)² - (3a²)³

(7-3a²)³ = 343-441a²+189a⁴-27a⁶

10)

(b+ab)³ = (b)³ + 3(b)²(ab) + 3(b)(ab)² + (ab)³

(b+ab)³ = b³+3ab³+3a²b³+a³b³

11)

(2y-x)³ = (2y)³ - 3(2y)²(x) + 3(2y)(x)² - (x)³

(2y-x)³ = 8y³-12y²x+6yx²-x³

12)

(3-4c)³ = (3)³ - 3(3)²(4c) + 3(3)(4c)² - (4c)³

(3-4c)³ = 27-108c+144c²-64c³