Question

Resuelva los siguientes productos notables:

Answer 1

A todos los ejercicios aplicas Propiedad Distributiva

$\bold{(a+1)(a+2)(x+2)(x+4)}\\ \\ \bold{(a*a+a*2+1*a+1*2)(x*x+x*4+2*x+2*4)}\\ \\ \bold{(a^{2}+2a+1a+2)(x^{2} +4x+2x+8)}\\ \\ \bold{(a^{2}+3a+2)(x^{2} +6x+8)}\qquad ahora \ volvemos \ distribuir\\ \\\\ \bold{(a^{2}x^{2} +a^{2}*6x+a^{2}*8+3a*x^{2}+3a*6x+3a*8+2*x^{2} +2*6x+2*8)}\\ \\ \boxed{\bold{(a^{2}x^{2} +6xa^{2}+8a^{2}+3ax^{2}+18ax+24a+2x^{2} +12x+16)}}$

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$\bold{(x+5)(x-2)}\\ \\ \bold{x*x+x*(-2)+5*x+5*(-2)}\\ \\ \bold{x^{2} -2x+5x-10}\\ \\ \boxed{\bold{x^{2} +3x-10}}$

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$\bold{(m-6)(m-5)}\\ \\ \bold{m*m+m*(-5)+(-6)*m+(-6)*(-5)}\\ \\ \bold{m^{2} -5m-6m+30}\\ \\ \boxed{\bold{m^{2} -11m+30}}$

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$\bold{(x+7)(x-3)}\\ \\ \bold{x*x+x*(-3)+7*x+7*(-3)}\\ \\ \bold{x^{2} -3x+7x-21}\\ \\ \boxed{\bold{x^{2} +4x-21}}$

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$\bold{(x+2)(x-1)}\\ \\ \bold{x*x+x*(-1)+2*x+2*(-1)}\\ \\ \bold{x^{2} -x+2x-2}\\ \\ \boxed{\bold{x^{2} +x-2}}$

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$\bold{(x-3)(x-1)}\\ \\ \bold{x*x+x*(-1)+(-3)*x+(-3)*(-1)}\\ \\ \bold{x^{2} -x-3x+3}\\ \\ \boxed{\bold{x^{2} -4x+3}}$

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$\bold{(x-5)(x+4)}\\ \\ \bold{x*x+x*4+(-5)*x+(-5)*(4)}\\ \\ \bold{x^{2} +4x-5x-20}\\ \\ \boxed{\bold{x^{2} -x-20}}$

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$\bold{(a-11)(a+10)}\\ \\ \bold{(a*a+a*10+(-11)*a+(-11)*10)}\\ \\ \bold{(a^{2}+10a-11a-110)}\\ \\ \boxed {\bold{(a^{2}-a-110)}}$

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$\bold{(n^{2}-1)(n^{2}+20)}\\ \\ \bold{(n^{2}* n^{2}+n^{2}*20-1n^{2} +(-1)*20}\\ \\ \bold{(n^{4}+20n^{2}-n^{2}-20)}\\ \\ \boxed {\bold{(n^{4}+19n^{2} -20)}}$

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Espero que te sirva, salu2!!!!