Aplicar las fórmulas de productos notables y hallar el producto indicado:
Respuestas a la pregunta
1. Resolver: (3x - 2)² + (3x - 2)(3x + 2)
Fórmulas a aplicar:
(a ± b)² = a² ± 2ab + b²
(a + b)(a - b) = a² - b²
(3x - 2)² + (3x - 2)(3x + 2) = (3x)² - 2(3x)(2) + (2)² + (3x)² - (2)² ⇒
(3x - 2)² + (3x - 2)(3x + 2) = 18x² - 12x
2. Resolver: (5x + 2)(5x - 2) + (x - 5)(x + 6)
Fórmulas a aplicar:
(a + b)(a - b) = a² - b²
(a ± b)(a ± c) = a² + (±b ± c)a + (±b)(±c)
(5x + 2)(5x - 2) + (x - 5)(x + 6) = (5x)² - (2)² + (x)² + (-5 + 6)x + (-5)(6) ⇒
(5x + 2)(5x - 2) + (x - 5)(x + 6) = 26x² + x - 34
3. Resolver: (9x + 2)² + (3x - 5)(3x - 5)(3x - 5)
Fórmulas a aplicar:
(a ± b)² = a² ± 2ab + b²
(a ± b)³ = a³ ± 3a²b + 3ab² ± b³
(9x+2)²+(3x-5)³ = (9x)² + 2(9x)(2) + (2)² + (3x)³ - 3(3x)²(5) + 3(3x)(5)² - (5)³ ⇒
(9x + 2)² + (3x - 5)³ = 27x³ + 36x² + 261x - 121
4. Aplicar productos notables: (2x - 3y)³ - (x + 5)(x - 5)
Fórmulas a aplicar:
(a ± b)² = a² ± 2ab + b²
(a + b)(a - b) = a² - b²
(2x - 3y)³ - (x + 5)(x - 5) = (2x)² - 2(2x)(3y) + (3y)² - ((x)² - (5)²) ⇒
(2x - 3y)³ - (x + 5)(x - 5) = 3x² - 12xy + 9y² + 25
5. Aplicar productos notables: (2x - y)² - (x + 5)²
Fórmulas a aplicar:
(a ± b)² = a² ± 2ab + b²
(2x - y)² - (x + 5)² = (2x)² - 2(2x)(y) + (y)² - ((x)² + 2(x)(5) + (5)²) ⇒
(2x - y)² - (x + 5)² = 3x² - 10x - 4xy + y² - 25
6. Simplificar: (2x - y)(x² - 15x + 5) - 3x(x + 4)
Fórmulas a aplicar: propiedad distributiva del producto en ambos términos.
(2x-y)(x²-15x+5)-3x(x+4)=(2x)(x²)-(2x)(15x)+(2x)(5)-(y)(x²)+(y)(15x)-(y)(5)-(3x)(x)-(3x)(4) ⇒
(2x - y)(x² - 15x + 5) - 3x(x + 4) = 3x³ - 33x² - yx² - 2x + 15yx - 5y