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a) \(\left(a+b+c-d\right).\left(a+b-c+d\right)=\left(a+b\right)^2-\left(c-d\right)^2\)
b) \(\left(a+b-c-d\right).\left(a-b+c-d\right)=\left(a-d\right)^2-\left(b-c\right)^2\)
Dùng hằng đẳng thức để tính
a) \(\left(a+b+c-d\right).\left(a+b-c+d\right)\)
\(=\left(a+b\right)^2-\left(c-d\right)^2.\)
b) \(\left(a+b-c-d\right).\left(a-b+c-d\right)\)
\(=\left(a-d\right)^2-\left(b-c\right)^2.\)
Chúc bạn học tốt!
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a: \(=\left(a+b\right)^2-\left(c+d\right)^2\)
b: \(=\left(a-d\right)^2-\left(b-c\right)^2\)
c: \(=\left(x+3z\right)^2-4y^2\)
d: \(=\left(a^2-9\right)\left(a^2+9\right)=a^4-81\)
e: \(=\left(a-5\right)^2\cdot\left(a+5\right)^2=\left(a^2-25\right)^2\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a² + b² + c² + d² + e² ≥ a(b + c + d + e)
Ta có: a² + b² + c² + d² + e²
= (a²/4 + b²) + (a²/4 + c²) + (a²/4 + d²) + (a²/4 + e²)
Lại có: (a/2 - b)² ≥ 0 <=> a²/4 - ab + b² ≥ 0 <=> a²/4 + b² ≥ ab
Tương tự ta có:
. a²/4 + c² ≥ ac
. a²/4 + d² ≥ ad
. a²/4 + e² ≥ ae
--> (a²/4 + b²) + (a²/4 + c²) + (a²/4 + d²) + (a²/4 + e²) ≥ ab + ac + ad + ae
<=> a² + b² + c² + d² + e² ≥ a(b + c + d + e) --> đ.p.c.m
Dấu " = " xảy ra <=> a/2 = b = c = d = e
P/s: Hơi hơi dễ nhỉ
![](https://rs.olm.vn/images/avt/0.png?1311)
=(ab+ac+b^2+bc)- (cd+ca+d^2+ad)-(ab-ad+cb-cd)
=ab+ac+b^2+bc-cd-ca-d^2-ad-ab+ad-cb+cd
=b^2-d^2
\(\left(a+b\right)\left(b+c\right)-\left(c+d\right)\left(d+a\right)-\left(a+c\right)\left(b-d\right)\)
\(=\left(ab+ac+b^2+bc\right)-\left(cd+ac+d^2+ad\right)-\left(ab-ad+bc-cd\right)\)
\(=ab+ac+b^2+bc-cd-ac-d^2-ad-ab+ad-bc+cd\)
\(=b^2-d^2.\)
Vậy \(\left(a+b\right)\left(b+c\right)-\left(c+d\right)\left(d+a\right)-\left(a+c\right)\left(b-d\right)=b^2-d^2\).
![](https://rs.olm.vn/images/avt/0.png?1311)
a) x2 - 2xy + y2 - 4m2 + 4mn - n2 = (x - y)2 - [(2m)2 - 2.2m.n + n2] = (x - y)2 - (2m - n)2
= [(x - y) - (2m - n)][(x - y) + (2m - n)] = (x - y - 2m + n)(x - y + 2m - n)
b) x2 - 4x2y2 + y2 + 2xy = x2 + 2xy + y2 - 4x2y2 = (x + y)2 - (2xy)2 = (x + y - 2xy)(x + y + 2xy)
c) x6 - y6 = (x3)2 - (y3)2 = (x3 - y3)(x3 + y3) = (x - y)(x2 + xy + y2)(x + y)(x2 - xy - y2)
d) 25 - a2 + 2ab - b2 = 25 - (a2 - 2ab + b2) = 52 - (a - b)2 = (5 - a + b)(5 + a - b)
a) ((a+b)+(c+d)).((a+b)-(c+d) )
=(a+b)^2-(c+d)^2
=(a^2+2ab+b^2)-(c^2+2cd+d^2)
=a^2+2ab+b^2-c^2-2cd-d^2