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Bổ sung nha :
(x - y)2 - (2m - n)2
= (x - y -2m - n) . (x - y + 2m - n) .
Chúc bạn học tốt !
x2-2xy+y2-4m2+4mn-n2 mới đúng tui giải cho
<=> (x-y)2-(4m-n)2< Áp dụng hằng đẳng thức số 2 >
<=> (x-y-4m-2).(x-y+4m-2) < HĐT số 3 >
\(-16a^4b^6-24a^5b^5-9a^6b^4\)
\(=-a^4b^4\left(16b^2+24ab+9a^2\right)\)
\(=-a^4b^4\left[\left(4b\right)^2+2\cdot4\cdot3\cdot ab+\left(3a\right)^2\right]\)
\(=-a^4b^4\cdot\left(3a+4b\right)^2\)
\(a^4\left(b-c\right)+b^4\left(c-a\right)+c^4\left(a-b\right)\)
\(=a^4\left(b-c\right)+b^4[\left(c-b\right)-\left(a-b\right)]+c^4\left(a-b\right)\)
\(=a^4\left(b-c\right)+b^4\left(c-b\right)-b^4\left(a-b\right)+c^4\left(a-b\right)\)
\(=a^4\left(b-c\right)-b^4\left(b-c\right)-b^4\left(a-b\right)+c^4\left(a-b\right)\)
\(=\left(b-c\right)\left(a^4-b^4\right)-\left(a-b\right)\left(c^4-b^4\right)\)
\(=\left(b-c\right)\left(a^2-b^2\right)\left(a^2+b^2\right)-\left(a-b\right)\left(c^2-b^2\right)\left(c^2+b^2\right)\)
\(=\left(b-c\right)\left(a-b\right)\left(a+b\right)\left(a^2+b^2\right)+\left(a-b\right)\left(b-c\right)\left(c+b\right)\left(c^2+b^2\right)\)
\(=\left(b-c\right)\left(a-b\right)[\left(a+b\right)\left(a^2+b^2\right)+\left(c+b\right)\left(c^2+b^2\right)]\)
a: \(4x^2-4x\)
\(=4x\cdot x-4x\cdot1\)
\(=4x\left(x-1\right)\)
b: \(x^2-2xy+y^2-4\)
\(=\left(x-y\right)^2-2^2\)
\(=\left(x-y-2\right)\left(x-y+2\right)\)
\(2x^3-3x^2+3x-1=x^3+x^3-3x^2+3x-1\)
=\(x^3+\left(x^3-3x^2+3x-1\right)\)=\(x^3+\left(x-1\right)^3\)
=\(\left(x+x-1\right)\left(x^2-x\left(x-1\right)+\left(x-1\right)^2\right)\)
=\(\left(2x-1\right)\left(x^2-x^2+x+x^2-2x+1\right)\)
=\(\left(2x-1\right)\left(x^2-x+1\right)\)
\(a^4+a^2+1\)
\(=a^4-a+a^2+a+1\)
\(=a\left(a^3-1\right)+\left(a^2+a+1\right)\)
\(=a\left(a-1\right)\left(a^2+a+1\right)+\left(a^2+a+1\right)\)
\(=\left(a^2+a+1\right)\left[a\left(a-1\right)+1\right]\)
\(=\left(a^2+a+1\right)\left(a^2-a+1\right)\)
a4 + a2 +1 = a4 +2a2 + 1 - a2
= (a4 +2a2 + 1) - a2
= (a2 + 1)2 - a2
= (a2 + 1 - a)(a2 + 1 +a)