Запишите алгебраическое выражение в виде многочлена стандартного вида: а)8-(2+a)(3a+4)...

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

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+3a²+4a = 3a²+6a+4a+8 = 3a²+10a+8 = -(3a²+10a+8)=-(3a²)-(10a)-(8) = -3a²-10a-8 = -3a²-10a+8-8 = -3a²-10a

б) 2a³+(a+a²)(5-2a) = (a+a²)(5-2a) = a*5+a(-2a)+a²*5+a²(-2a) = a*5-a*2a+a²*5-a²*2a = 5a-2a²+5a²-2a²a = 5a-2a²+5a²-2a³ = 5a+3a³-2a³ = 2a³+5a+3a²-2a³ = 3a²+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-2x² = 2-2x² = 2-2x²+(2-x)(1-2x) = 2*1+2(-2x)-x*1-x(-2x) = 2*1-2*2x-x*1+x*2x = 2-4x-x+2x² = 2-5x+2x² = 2-2x²+2-5x+2x² = -2x²+2x²-5x+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 = x²-7x+2*5 = x²-7x+10 = x²-7x+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 = x²-7x+3*4 = x²-7x+12 = -(x²-7x+12) = -(x²)-(-7x)-(12) = -x²+7x-12 = x²-7x+10-x²+7x-12 = x²-x²-7x+7x+10-12 = x²-x²+10-12 = 10-12 = -2

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а) 3(x-4)+x²-4x = 3x-12+x²-4x = x²-x-12 = (x+3)(x-4)
б) 2x-8-x(x-4) = 2x-8-x²+4x = -x²+6-8 = -(x-2)(x-4)
в) x³+5x²-2x-10 = x²(x-5)-2(x+5) =(x+5)(x²-2) = (x+5)(x+√2)(x-√2)
г) x³-6x²-2x+12 = x²(x-6)-2(x-6) = (x-6)(x²-2) = (x-6)(x+√2)(x-√2)