\(2xy^2+x^2y^4+1\)

\(=\left(xy^2\right)^2+2.xy^2+1^2\)

\(=\left(xy^2+1\right)^2\)

làm sai bét

a) Dễ chứng minh \(\Delta\)DKA = \(\Delta\)BMA.

Suy ra ^KAD = ^MAB. Mà ^MAB + ^MAN + ^NAD = 90^o

Nên ^KAD + ^MAN + ^NAD = 90^o hay ^KAD + ^NAD = 45^o hay ^KAN = 45^o

b)Chưa nghĩ ra

Giúp em với mấy anh chị~"

= \(-2x^2-2.\frac{1,5.\sqrt{2}.x}{\sqrt{2}}-\frac{2.25}{2}+6.125\)

= \(6.125-\left(\sqrt{2}x-\frac{1.5}{\sqrt{2}}\right)^2\le6.125\forall x\)

=> GTLN của bt là 6.125 khi  x=0.75

a/\(\left(x-1\right)\left(x^5+x^4+x^3+x^2+x+1\right).\)

\(=\left(x-1\right)\left[\left(x^5+x^4+x^3\right)+\left(x^2+x+1\right)\right]\)

\(=\left(x-1\right)\left[x^3\left(x^2+x+1\right)+\left(x^2+x+1\right)\right]\)

\(=\left(x-1\right)\left(x^2+x+1\right)\left(x^3+1\right)\)

\(=\left(x-1\right)\left(x^2+x+1\right)\left(x+1\right)\left(x^2-x+1\right)\)

\(=\left(x-1\right)\left(x+1\right)\left(x^2-x+1\right)\left(x^2+x+1\right)\)

\(=\left(x^2-1\right)\left(x^2-x+1\right)\left(x^2+x+1\right)\)

Câu b/ quên làm ạ :> Bù nè

b/ \(2\left(3x-1\right)\left(2x+5\right)-\left(4x-1\right)\left(3x-2\right)\)

\(=2\left(6x^2+15x-2x-5\right)-\left(12x^2-8x-3x+2\right)\)

\(=2\left(6x^2+13x-5\right)-\left(12x^2-11x+2\right)\)

\(=12x^2+26x-10-\left(12x^2-11x+2\right)\)

\(=12x^2+26x-10-12x^2+11x-2\)

\(=37x-12\)

B = (x + 2)³ + (x - 2)³ - 2x(2x² + 12)

B = (x + 2)(x² + 2x.2 + 2²) + (x - 2)(x² - 2x.2 + 2²) - 2x(2x³ + 12)

B = x³ + 4x³ + 4x + 2x² + 8x + 8 + x³ - 4x² + 4x - 2x² + 8x - 8 - 4x³ - 24x

B = -2x³

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