Запишите алгебраическое выражение в виде многочлена стандартного вида:
а)8-(2+a)(3a+4)
б)2a^3+(a+a^2)(5-2a)
в)(1-x)(2+2x)+(2-x)(1-2x)
г)(x-2)(x-5)-(x-3)(x-4)
Разложите нв множители алгебраическое выражение:
а)3(x-4)+x^2-4x
б)2x-8-x (x-4)
в)x^3+5x^2-2x-10
г)x^3-6x^2-2x+12

Первое задание:
$a)\,\,\,8-(2+a)(3a+4)=8-(6a+8+3a^2+4a)=8-6a-8-3a^2-\\\\-4a=\boxed{-3a^2-10a}\\\\\\b)\,\,\,2a^3+(a+a^2)(5-2a)=2a^3+5a-2a^2+5a^2-2a^3=\\\=\boxed{3a^2+5a}\\\\\\c)(1-x)(2+2x)+(2-x)(1-2x)=2+2x-2x-2x^2+2-4x-\\\\-x+2x^2=\boxed{4-5x}\\\\\\d)\,\,\,(x-2)(x-5)-(x-3)(x-4)=x^2-5x-2x+10-(x^2-4x-\\\\-3x+12)=x^2-7x+10-x^2+4x+3x-12=\boxed{-2}$

Второе задание:
$a)\,\,\,3(x-4)+x^2-4x=3(x-4)+x(x-4)=\boxed{(x-4)(3+x)}\\\\\\b)\,\,\,2x-8-x (x-4) =2(x-4)-x(x-4)=\boxed{(x-4)(2-x)}\\\\\\c)\,\,\,x^3+5x^2-2x-10=x^2(x+5)-2(x+5)=(x+5)(x^2-2)=\\\=\boxed{(x+5)(x-\sqrt2)(x+\sqrt2)}\\\\\\d)\,\,\,x^3-6x^2-2x+12=x^2(x-6)-2(x-6)=(x-6)(x^2-2)=\\\=\boxed{(x-6)(x-\sqrt2)(x+\sqrt2)}$

Оцени ответ

Расписываю всё подробно:
а) 8-(2+a)(3a+4) = (2+a)(3a+4) = 2*3a+2*4*a*3a+a*4 = 6a+2*4+3aa+4a = 6a+8+3aa+4a = 6a+8+3a?+4a = 3a?+6a+4a+8 = 3a?+10a+8 = -(3a?+10a+8)=-(3a?)-(10a)-(8) = -3a?-10a-8 = -3a?-10a+8-8 = -3a?-10a

б) 2a?+(a+a?)(5-2a) = (a+a?)(5-2a) = a*5+a(-2a)+a?*5+a?(-2a) = a*5-a*2a+a?*5-a?*2a = 5a-2a?+5a?-2a?a = 5a-2a?+5a?-2a? = 5a+3a?-2a? = 2a?+5a+3a?-2a? = 3a?+5a

в) (1-x)(2+2x)+(2-x)(1-2x) = (1-x)(2+2x) = 1*2+1*2x-x*2-x*2x = 2+2x-2x-2xx = 2+2x-2x-2x? = 2-2x? = 2-2x?+(2-x)(1-2x) = 2*1+2(-2x)-x*1-x(-2x) = 2*1-2*2x-x*1+x*2x = 2-4x-x+2x? = 2-5x+2x? = 2-2x?+2-5x+2x? = -2x?+2x?-5x+2+2 = -5x+2+2 = -5x+4

г) (x-2)(x-5)-(x-3)(x-4) = (x-2)(x-5) = x*x+x(-5)-2*x-2(-5) = xx*x*5-2x+2*5 = xx-7x+2*5 = x?-7x+2*5 = x?-7x+10 = x?-7x+10-(x-3)(x-4) = (x-3)(x-4) = x*x+x(-4)-3*x-3(-4) = xx-x*4-3x+3*4 = xx-x*4-3x+3*4 = xx-7x+3*4 = x?-7x+3*4 = x?-7x+12 = -(x?-7x+12) = -(x?)-(-7x)-(12) = -x?+7x-12 = x?-7x+10-x?+7x-12 = x?-x?-7x+7x+10-12 = x?-x?+10-12 = 10-12 = -2

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а) 3(x-4)+x?-4x = 3x-12+x?-4x = x?-x-12 = (x+3)(x-4)
б) 2x-8-x(x-4) = 2x-8-x?+4x = -x?+6-8 = -(x-2)(x-4)
в) x?+5x?-2x-10 = x?(x-5)-2(x+5) =(x+5)(x?-2) = (x+5)(x+v2)(x-v2)
г) x?-6x?-2x+12 = x?(x-6)-2(x-6) = (x-6)(x?-2) = (x-6)(x+v2)(x-v2)