Question

CM các hằng đẳng thức sau

a, ( a - b )² = ( a + b )² - 4ab

b, ( a + b + c )² + a² + b² + c² = ( c+ b )² + ( b + c )² + ( a + c )²

c, x⁴ + y⁴ + ( x + y )⁴ = 2( x² = xy + y² )²

d, ( 5a - 3b - 8c ) = ( 3a - 5b ) biết a² - b² = 4c²

Answer 1

\(a.\) \(\left(a-b\right)^2=\left(a+b\right)^2-4ab\)

\(\left(a-b\right)^2+2ab-2ab=\left(a+b\right)^2-4ab\)

\(\left(a-b\right)^2=a^2+2ab+b^2-4ab\)

\(\left(a-b\right)^2=a^2-2ab+b^2\)

\(\left(a-b\right)^2=\left(a-b\right)^2\)

Vậy \(\left(a-b\right)^2=\left(a+b\right)^2-4ab\)

Tương tự mấy câu kia

Answer 2

b: \(\left(a+b+c\right)^2+a^2+b^2+c^2\)

\(=2a^2+2b^2+2c^2+2ab+2bc+2ac\)

\(=\left(a^2+2ab+b^2\right)+\left(b^2+2bc+c^2\right)+\left(a^2+2ac+c^2\right)\)

\(=\left(a+b\right)^2+\left(b+c\right)^2+\left(a+c\right)^2\)

c: \(x^4+y^4-2\left(x^2+xy+y^2\right)^2\)

\(=\left(x^2+y^2\right)^2-2x^2y^2-2\left[\left(x^2+y^2\right)^2+2xy\left(x^2+y^2\right)+x^2y^2\right]\)

\(=-\left(x^2+y^2\right)^2-4x^2y^2-4xy\left(x^2+y^2\right)\)

\(=-\left(x^2+2xy+y^2\right)^2=-\left(x+y\right)^4\)

=>\(x^4+y^4+\left(x+y\right)^4=2\left(x^2+xy+y^2\right)^2\)