(x+2)(x+3)(x+4)(x+5)-24

=[(x+2)(x+5)][(x+3)(x+4)-24

=(x²+5x+2x+10)(x²+7x+12)-24

=(x2+7x+11-1)(x²+7x+11+1)

=(x²+7x+11)²-1²-24

=(x²+7x+11)²-5²

=(x²+7x+11+5)(x²+7x+11-5)

=(x²+7x+16)(x²+7x+6)

làm hộ mình các phần còn lại nhé!!

x^5+y^5=xxxxx+yyyyy=aaaaa

1)a²(b-c)+b²(c-a)+c²(a-b)

=a²b-a²c+b²c-b²a+c²a-c²b

=(a²b-c²b)+(b²c-b²a)+(c²a-a²c)

=b.(a²-c²)-b².(a-c)-ac.(a-c)

=b.(a-c)(a+c)-b²(a-c)-ac(a-c)

=(a-c)(ab+bc-b²-ac)

=(a-c)[(ab-ac)+(bc-b²)]

=(a-c)[a.(b-c)-b.(b-c)]

=(a-c)(b-c)(a-b)

a) x³ - 4x² + 12x - 27 = (x - 3)(x² + 3x + 9) - 4x(x - 3)

= (x - 3)(x² + 3x + 9 - 4x) = (x - 3)(x² - x + 9)

b) x³ + 2x² + 2x + 1 = (x + 1)(x² - x + 1) + 2x(x + 1)

= (x + 1)(x² - x + 1 + 2x) = (x + 1)(x² + x + 1)

c) y⁴ - 2y³ + 2y - 1 = (y² - 1)(y² + 1) - 2y(y² - 1)

= (y² - 1)(y² + 1 - 2y) = (y - 1)(y + 1)(y - 1)²

= (y + 1)(y - 1)³

\(A=\left[\left(a+b\right)+\left(c+d\right)\right]^2+\left[\left(a+b\right)-\left(c+d\right)\right]^2+\left[\left(a-b\right)+\left(c-d\right)\right]^2+\left[\left(a-b\right)-\left(c-d\right)\right]^2\)

Ta có

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

\(\left[\left(a+b\right)-\left(c+d\right)\right]^2=\left(a+b\right)^2-2\left(a+b\right)\left(c+d\right)+\left(c+d\right)^2\)

\(\left[\left(a-b\right)+\left(c-d\right)\right]^2=\left(a-b\right)^2+2\left(a-b\right)\left(c-d\right)+\left(c-d\right)^2\)

\(\left[\left(a-b\right)-\left(c-d\right)\right]^2=\left(a-b\right)^2-2\left(a-b\right)\left(c-d\right)+\left(c-d\right)^2\)

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

\(A=2\left(a^2+2ab+b^2+a^2-2ab+b^2+c^2+2cd+d^2+c^2-2cd+d^2\right)\)

\(A=4\left(a^2+b^2+c^2+d^2\right)\)

y^4+4

=y^4+2^2

=(y^2)^2+2^2

=(y^2+2)^2-2.y^2.2

=(y^2+2)^2-4y^2

=(y^2+2)^2-(2y)^2=(y^2+2-2y)(y^2+2+2y)