Question

Realiza el siguiente producto notable (a+2)(a-3)(a-2)(a+3)
B)
$(6x {}^{2} - m {}^{2} x)(6x + m {}^{2} x) \\ c)(a {}^{x + 1} - 2b {}^{x - 1} )(2b {}^{x - 1} + a {}^{x + 1} )$
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Answer 1

Respuesta:

$(a+2)(a-3)(a-2)(a+3)=a^{4}+-13a^{2}+36$

$(6x^{2}-m^{2}x)(6x+m^{2}x)=-mx^{4}x^{2}-6m^{2} x^{3}+6x^{2}m^{2}x-36x^{3}$

$\left(a^{x+1}-2bx^{x-1}\right)\left(2bx^{x-1}+a^{x+1}\right)=a^{2x+2}-4b^{2}x^{2x-2}$

Explicación paso a paso:

$(a+2)(a-3)(a-2)(a+3)\\=(a+2)(a-2)(a+3)(a-3) \quad \text{conmutatividad}\\=(a^{2}-4)(a^{2}-9) \quad \text{binomios conjugados}\\=a^{4}+(-4-9)a^{2}+(-4)(-9) \quad \text{binomios con termino comun}\\=a^{4}+-13a^{2}+36$

$(6x^{2}-m^{2}x)(6x+m^{2}x)\\= -(-6x^{2}+m^{2}x)(6x+m^{2}x)\\= -(mx^{4}x^{2}+(6x-6x^{2})m^{2}x+(6x)(6x^{2})\\=-(mx^{4}x^{2}+6m^{2} x^{3}-6x^{2}m^{2}x+36x^{3})\\=-mx^{4}x^{2}-6m^{2} x^{3}+6x^{2}m^{2}x-36x^{3}$

$\left(a^{x+1}-2bx^{x-1}\right)\left(2bx^{x-1}+a^{x+1}\right)\\=\left(a^{x+1}-2bx^{x-1}\right)\left(a^{x+1}+2bx^{x-1}\right)\\=\left(a^{x+1}\right)^{2}-\left(2bx^{x-1}\right)^{2}\\=a^{2x+2}-4b^{2}x^{2x-2}$