Aplicar las fórmulas de productos notables y hallar el producto indicado ?

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 - 12x2.

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 - 343.

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 - 1214.

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 + 255.

Aplicar productos notables : (2x - y)² - (x + 5)²Fórmulas 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 - 256.

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.