\(a^4+a^2+1=\left(a^4+2a^2+1\right)-a^2=\left(a^2+1\right)^2-a^2=\left(a^2+1-a\right)\left(a^2+1+a\right).\)

Ta có x⁴ + x² + 1 = (x⁴ + x³ + x²) + (- x³ - x² - x) + ( x² + x + 1) = x²( x² + x + 1) - x( x² + x + 1) + ( x² + x + 1) 

= ( x² + x + 1)(x² - x + 1)

192837465 + 918273645 = 9999999990

K MK NHA

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a) \(\left(x+y\right)^2+x^2-y^2\)

\(\left(x+y\right)^2+\left(x+y\right)\left(x-y\right)\)

\(=\left(x+y\right)\left(x+y+x-y\right)\)

\(=2x\left(x+y\right)\)

Thay x=69 và y=31 vào 2x(x+y), ta có:

\(2.69\left(69+31\right)=138.100=13800\)

\(a\left(b^3-c^3\right)+b\left(c^3-a^3\right)+c\left(a^3-b^3\right)\)

\(=a\left[-\left(a^3-b^3\right)-\left(c^3-a^3\right)\right]+b\left(c^3-a^3\right)+c\left(a^3-b^3\right)\)

\(=-a\left(a^3-b^3\right)+c\left(a^3-b^3\right)+b\left(c^3-a^3\right)-a\left(c^3-a^3\right)\)

\(=\left(a^3-b^3\right)\left(c-a\right)+\left(c^3-a^3\right)\left(b-a\right)\)

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

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

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

\(=\left(a-b\right)\left(c-a\right)\left(b-c\right)\left(a+b+c\right)\)

Có: \(AB=BC.\sin C\)

\(\Rightarrow AB=10.\sin\left(30^{\text{o}}\right)\)

\(\Rightarrow AB=5\)

Đơn vị k rõ

AB=BC*cosB=10*1/2=5

(a+b+c)3−a3−b3−c3(a+b+c)3−a3−b3−c3

=a3+3a2(b+c)+3a(b+c)2+(b+c)3−a3−b3−c3=a3+3a2(b+c)+3a(b+c)2+(b+c)3−a3−b3−c3

=3(b+c)(a2+ab+ac)+b3+3b2c+3bc2+c3−b3−c3=3(b+c)(a2+ab+ac)+b3+3b2c+3bc2+c3−b3−c3

=3(b+c)(a2+ab+ac+bc)=3(b+c)(a2+ab+ac+bc)

=3(b+c)[a(a+b)+c(a+b)]=3(b+c)[a(a+b)+c(a+b)]

=3(b+c)(a+b)(a+c)