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a) a3+b3+a2c+b2c-abc
= (a+b)(a2-ab+b2)+c(a2+b2)-abc
=(a+b) [ (a+b)2-3ab]+c.[(a+b)2-2ab]-abc
=(a+b)(a+b)2-3ab(a+b)+c(a+b)2-3abc
=(a+b)2(a+b+c)-3ab(a+b+c)
=(a+b)2.0-3ab.0
=0
b) ax+ay+2x+2y+4
=a(x+y)+2(x+y)+4
=(x+y)(a+2)+4
=(a-2)(a+2)+4
=a2-4+4
=a2
c) A=1+x+x2+...+x49=>Ax=x+x2+x3+...+x50
- A=1+x+x2+...+x49
---> Ax-A=x50-1
d)(a+b)(a+c)+(c+a)(c+b)
=a2+ac+ab+bc+c2+bc+ac+ab
=a2+c2+2ac+2ab+2bc
=2b2+2bc+2ac+2ab
=2b(b+c)+2a(b+c)
=2b(b+c)(b+a)
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1) x - y - a(x - y) = (x - y) - a(x - y) = (1 - x)(x - y)
2) a - b + x(a - b) = (a - b) + x(a - b) = (1 + x)(a - b)
3) a(x - y) - x + y = a(x - y) - (x - y) = (a - 1)(x - y)
4) x(a - b) - a + b = x(a - b) - (a - b) = (x - 1)(a - b)
5) ax + ay + bx + by = a(x + y) + b(x + y) = (a + b)(x + y)
6) ax + ay - bx - by = a(x + y) - b(x + y) = (a - b)(x + y)
7) - 2x - 2y + ax + ay = -2(x + y) + a(x + y) = (a - 2)(x + y)
8) x2 - xy - 2x + 2y = x(x - y) - 2(x - y) = (x - 2)(x - y)
Sorry nha, giờ mình chỉ rảnh làm 8 câu thôi
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\(a,7x^2-7xy-4x+4y\)
\(=7x\left(x-y\right)-4\left(x-y\right)\)
\(=\left(7x-4\right)\left(x-y\right)\)
\(b,2x-2y+ax-ay\)
\(=2\left(x-y\right)+a\left(x-y\right)\)
\(=\left(a+2\right)\left(x-y\right)\)
\(c,x^2-x-y^2-y\)
\(=\left(x^2-y^2\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y-1\right)\)
\(d,ax+ay-2x-2y\)
\(=a\left(x+y\right)-2\left(x+y\right)\)
\(=\left(a-2\right)\left(x+y\right)\)
\(e,x\left(a+b\right)-a-b=x\left(a+b\right)-\left(a+b\right)\)
\(=\left(x-1\right)\left(a+b\right)\)
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b) VT=ax+2x+ay+2y+4=a\(^2\)
=a(x+y)+2(x+y)+4
=a(a-2)+2(a-2)+4
=\(a^2\)-2a+2a-4+4=a\(^2\)=VP
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Bạn chỉ việc nhân ra ròi cho nó bằng hệ số của từng cái là đc thôi
\(ax+2x+ay+2y+4=x\left(a+2\right)+y\left(a+2\right)+4=\left(a+2\right)\left(x+y\right)+4=\left(a+2\right)\left(a-2\right)+4=a^2-4+4=a^2\)
từ a-2=x+y => y=a-2-x