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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 >
\(-16a^4b^6-24a^5b^5-9a^6b^4\)
\(=-a^4b^4\left(16b^2+24ab+9a^2\right)\)
\(=-a^4b^4\left[\left(4b\right)^2+2\cdot4\cdot3\cdot ab+\left(3a\right)^2\right]\)
\(=-a^4b^4\cdot\left(3a+4b\right)^2\)
\(2x^3-3x^2+3x-1=x^3+x^3-3x^2+3x-1\)
=\(x^3+\left(x^3-3x^2+3x-1\right)\)=\(x^3+\left(x-1\right)^3\)
=\(\left(x+x-1\right)\left(x^2-x\left(x-1\right)+\left(x-1\right)^2\right)\)
=\(\left(2x-1\right)\left(x^2-x^2+x+x^2-2x+1\right)\)
=\(\left(2x-1\right)\left(x^2-x+1\right)\)
\(x^4-5x^2+4\)
=\(\left(x^4-x^2\right)-\left(4x^2-4\right)\)
=\(x^2\left(x^2-1\right)-4\left(x^2-1\right)\)
=\(\left(x^2-4\right)\left(x^2-1\right)\)
\(x^2+5x-6\)
=\(x^2-x+6x-6\)
=\(x\left(x-1\right)+6\left(x-1\right)\)
=\(\left(x+6\right)\left(x-1\right)\)
2 câu cuối làm tương tự nha câu 2 nha
\(a\left(a+2b\right)^3-b\left(2a+b\right)^3\)
\(=a\left(a ^3+3.a^22b+3.a2b^2+2b^3\right)-b\left(2a^3+3.2a^2.b+3.2a.b^2+b^3\right)\)
\(=a\left(a^3+6a^2b+6ab^2+8b^3\right)-b\left(8a^3+6a^2b+6ab^2+b^3\right)\)
\(=a^4+6a^3b+6a^2b^2+8ab^3-8a^3b-6a^2b^2-6ab^3-b^4\)
\(=a^4+6a^3b+8ab^3-8a^3b-6ab^3-b^4\)
\(a\left(a+2b\right)^3-b\left(2a+b\right)^3\)
\(=a\left(a^3+6a^2b+12ab^2+8b^3\right)-b\left(8a^3+12a^2b+6ab^2+b^3\right)\)
\(=a^4+6a^3b+12a^2b^2+8ab^3-8a^3b-12a^2b^2-6ab^3-b^4\)
\(=a^4-2a^3b+2ab^3-b^4\)
\(=\left(a^2-b^2\right)\left(a^2+b^2\right)-2ab\left(a^2-b^2\right)\)
\(=\left(a^2-b^2\right)\left(a^2-2ab+b^2\right)\)
\(=\left(a+b\right)\left(a-b\right)^3\)
\(G=2x^2-3x+1=2x^2-2x-x+1\)
\(=2x\left(x-1\right)-\left(x-1\right)=\left(2x-1\right)\left(x-1\right)\)
\(H=-x^2+5x-4=-x^2+4x+x-4\)
\(=-x\left(x-4\right)+\left(x-4\right)=\left(1-x\right)\left(x-4\right)\)
\(I=x^2+4x+3=x^2+3x+x+3\)
\(=x\left(x+3\right)+\left(x+3\right)=\left(x+1\right)\left(x+3\right)\)
\(K=2x^2+7x+5=2x^2+2x+5x+5\)
\(=2x\left(x+1\right)+5\left(x+1\right)=\left(2x+5\right)\left(x+1\right)\)
\(L=-3x^2-5x-2=-3x^2-3x-2x-2\)
\(=-3x\left(x+1\right)-2\left(x+1\right)=\left(-3x-2\right)\left(x+1\right)\)
G = 2x2 - 3x +1 = 2x2 -2x -x +1 =(x-1).(2x-1)
H = -x2 + 5x - 4 = -x2 + 4x +x-4 = (x-4).(1-x)
I = x2 + 4x + 3 = x2 + 3x + x + 3 =(x+3).(x+1)
K = 2x2 + 7x + 5 = 2x2 + 2x + 5x + 5 = (x+1).(2x+5)
L = -3x2 -5x -2 = -3x2 - 3x - 2x - 2 = -3.x(x+1) - 2.(x+1) = (x+1).(-3x-2)
ko ghi lại đề nha:
=(5x2-10x)+5y2-5z
=5(x-2)+5y2-5z
mk chỉ làm đc đến đây thôi
\(a^4+a^2+1\)
\(=a^4-a+a^2+a+1\)
\(=a\left(a^3-1\right)+\left(a^2+a+1\right)\)
\(=a\left(a-1\right)\left(a^2+a+1\right)+\left(a^2+a+1\right)\)
\(=\left(a^2+a+1\right)\left[a\left(a-1\right)+1\right]\)
\(=\left(a^2+a+1\right)\left(a^2-a+1\right)\)
a4 + a2 +1 = a4 +2a2 + 1 - a2
= (a4 +2a2 + 1) - a2
= (a2 + 1)2 - a2
= (a2 + 1 - a)(a2 + 1 +a)