Question

Hola, necesito ayuda con lo siguiente, (se utilizando la fórmula de binomio al cuadrado y conjugado)

cuadrado:

(5a+2)²=

(4a²+2b)²=

(11x+7y³)²=

(4c⁴+5cd)²

conjugado:

(a+2)(a-2)=

(7a²-3b)(7a²+3b)=

(6ab+2cd)(6ab-2cd)=

(8a³b⁴+1)(8a³b⁴-1)=

(12x²-10)(12x²+10)=



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Answer 1

Explicación paso a paso:

Formula de binomio al  cuadrado:

(a ± b)² = a² ± 2ab + b²

Resolvamos:

(5a+2)² = (5a)² + 2(5a)(2) + (2)²

(5a+2)² = 25a²+20a+4

 

(4a²+2b)² = (4a²)² + 2(4a²)(2b) + (2b)²

(4a²+2b)² = 16a⁴+16a²b+4b²

 

(11x+7y³)² = (11x)² + 2(11x)(7y³) + (7y³)²

(11x+7y³)² = 121x²+154xy³+49y⁶

 

(4c⁴+5cd)² = (4c⁴)² + 2(4c⁴)(5cd) + (5cd)²

(4c⁴+5cd)² = 16c⁸+40c⁴cd+25c²d²

Formula de binomios conjugados:

(a + b)(a - b) = a² - b²

Resolvamos:  

(a+2)(a-2) = (a)² - (2)²

(a+2)(a-2) = a²-4  

(7a²-3b)(7a²+3b) = (7a²)² - (3b)²

(7a²-3b)(7a²+3b) = 49a⁴-9b²  

(6ab+2cd)(6ab-2cd) = (6ab)² - (2cd)²

(6ab+2cd)(6ab-2cd) = 36a²b²-4c²d²  

(8a³b⁴+1)(8a³b⁴-1) = (8a³b⁴)² - (1)²

(8a³b⁴+1)(8a³b⁴-1) = 64a⁶b⁸-1  

(12x²-10)(12x²+10) = (12x²)² - (10)²

(12x²-10)(12x²+10) = 144x⁴-100