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\(x^2-y^2+4x+4\)
\(=\left(x+2\right)^2-y^2\)
\(=\left(x+2+y\right)\left(x+2-y\right)\)
\(4x^2-y^2+8\left(y-2\right)\)
\(=4x^2-\left(y^2-8y+16\right)\)
\(=4x^2-\left(y-4\right)^2\)
\(=\left(2x+y-4\right)\left(2x-y+4\right)\)
\(a^3+a^2c-abc+b^2c+b^3\)
\(=\left(a^3+b^3\right)+\left(a^2c+b^2c-abc\right)\)
\(=\left(a+b\right)\left(a^2-ab+b^2\right)+\)\(c\left(a^2+b^2-ab\right)\)
\(=\left(a^2+b^2-ab\right)\left(a+b+c\right)\)
a) a3+a2c-abc+b2c+b3 =(a3+b3)+(a2c-abc+b2c)=(a+b)(a2-ab+b2)+c(a2-ab+b2)=(a2-ab+b2)(a+b-c)
b) x3-7x-6 = x3+x2-x2-x-6x-6=x2(x+1)-x(x+1)-6(x+1)=(x+1)(x2-x-6)=(x+1)(x-3)(x+2)
c) x3-x2-14x+24=x3-2x2+x2-2x-12x+24=x2(x-2)+x(x-2)-12(x-2)=(x-2)(x2+x-12)=(x-2)(x+4)(x-3)
\(A=a\left[\left(b-c\right)^2-a^2\right]+b\left[\left(c-a\right)^2-b^2\right]+c\left[\left(a-b\right)^2-c^2\right]+4abc\)
\(=a\left(b-c+a\right)\left(b-c-a\right)+b\left(c-a+b\right)\left(c-a-b\right)+c\left(a-b+c\right)\left(a-b-c\right)+4abc\)
\(=\left(a+b-c\right)\left(ab-ac-a^2-bc+ab-b^2\right)+c\left(a^2-2ab+b^2-c^2+4ab\right)\)
\(=\left(a+b-c\right)\left[-c\left(a+b\right)-\left(a-b\right)^2\right]+c\left[\left(a+b\right)^2-c^2\right]\)
\(=\left(a+b-c\right)\left(-ca-cb-a^2+2ab-b^2+ac+cb+c^2\right)\)
\(=\left(a+b-c\right)\left(c^2-\left(a-b\right)^2\right)\)
\(=\left(a+b-c\right)\left(c+a-b\right)\left(a+b-c\right)\)
= a^3.(b^2-c^2)+b^3.(c^2-b^2+b^2-a^2)+c^3.(a^2-b^2)
=a^3.(b^2-c^2) - b^3.(b^2-c^2 ) -b^3.(a^2-b^2)+c^3(a^2-b^2)
= (b^2 -c^2).(a^3-b^3) -(a^2-b^2).(b^3-c^3)
= (b-c)(b+c)(a-b)(a^2+ab+b^2)-(a-b)(a+b)(b-c)(b^2+bc +c^2)
=(b-c)(a-b).(b.a^2 +ab^2 +b^3 +ca^2 +abc +cb^2 - ab^2- abc - ac^2 - b^3-b^2 .c -bc^2)
=(b-c)(a-b)(a^2.b +ca^2 -ac^2-bc^2)
=(b-c)(a-b)(a-c)(ab+bc+ac)
còn dài hơn cả cách của mik ^^