Bài 1: CMR
a) (a2 + b2 ) (x2 + y2) = (ax - by)2 + (bx + ay)2
b) Nếu (a + b + c + d ) (a - b - c + d) = (a - b + c - d) ( a + b - c - d) thì \(\dfrac{a}{c}=\dfrac{b}{d}\) ( với a,b,c,d \(\ne\) 0 )
c) Nếu a + b + c = 4m thì 2ab + b2 + a2 - c2 = 16m2 - 8mc
d) Nếu (a - b)2 + (b - c)2 + (c - a)2 = 6abc thì a3 + b3 + c3 = 3abc (a + b + c +1)
a: \(\left(ax-by\right)^2+\left(bx+ay\right)^2\)
\(=a^2x^2-2axby+b^2y^2+b^2x^2+2abxy+a^2y^2\)
\(=a^2\left(x^2+y^2\right)+b^2\left(x^2+y^2\right)\)
\(=\left(x^2+y^2\right)\left(a^2+b^2\right)\)
c: \(a^2+2ab+b^2-c^2\)
\(=\left(a+b\right)^2-c^2\)
\(=\left(a+b+c\right)\left(a+b-c\right)\)
\(=4m\cdot\left(4m-2c\right)\)
\(=16m^2-8mc\)
