a: \(A=-x^2+4x+5\)

\(=-\left(x^2-4x-5\right)\)

\(=-\left(x^2-4x+4-9\right)\)

\(=-\left(x-2\right)^2+9\le9\)

Dấu '=' xảy ra khi x=2

b: \(B=-4x^2+12x-1\)

\(=-\left(4x^2-12x+1\right)\)

\(=-\left(4x^2-12x+9-8\right)\)

\(=-\left(2x-3\right)^2+8\le8\)

Dấu '=' xảy ra khi x=3/2

\(A=\left(x^2+9y^2+1-6xy+2x-6y\right)+\left(y^2+4y+4\right)+2\)

\(A=\left(x-3y+1\right)^2+\left(y+2\right)^2+2\ge2\)

\(A_{min}=2\) khi \(\left\{{}\begin{matrix}x=-7\\y=-2\end{matrix}\right.\)

\(B=\left(x^2+y^2+1-2xy+2x-2y\right)+\left(y^2+6y+9\right)+10\)

\(B=\left(x-y+1\right)^2+\left(y+3\right)^2+10\ge10\)

\(B_{min}=10\) khi \(\left\{{}\begin{matrix}x=-4\\y=-3\end{matrix}\right.\)

giúp mình với mình đang cần gấp

Để tính các biểu thức trên, ta sẽ áp dụng quy tắc nhân đa thức.

a) 2xy(3x+1) = 6x^2y + 2xy

b) -6x^2y(4x-5) = -24x^3y + 30x^2y

c) -3x^2(4x^2y-6xy) = -12x^4y + 18x^3y

d) 1/2xy^2(2x+3) = xy^2 + 3/2xy^2

e) 8x^2y^2(1/4xy-1/2x^2) = 2xy - 4x^2y^2

f) 5x(x^2+3x+1) = 5x^3 + 15x^2 + 5x

g) -1/2x^2y(2xy+6) = -x^3y - 3x^2y

bai2 :cmr

a, a^3+b^3=(a+b)^3-3ab.(a+b)

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

=\(a^3+b^3+3a^2b+3ab^2-3a^2b-3ab^2=a^3+b^3\)

=VT

b.a^3-b^3=(a-b)^3+3ab,(a-b)

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

=\(a^3-3a^2b+ab^2.3-b^3+3a^2b-3ab^2=a^3-b^3\)

=VT

=> ĐPCM

bài 1.

a) = 8x^3+4x^2y+2xy^2-4x^2y-2xy^2-y^3-(8x^3-4x^2y+2xy^2+4x^2y-2xy^2+y^3)

= 8x³+4x_²y+2xy_²-4x²y-2xy²-y³ - 8x³+4x²y-2xy²-4x²y+2xy²-y³

=-8x²y-6y³

b) = 27x³-18x²y+12xy²+18x²y-12xy²+8y³-27x³

=8y

đề bài đâu

a) (2xy+5)(4x^2+5): = 2xy * 4x^2 + 2xy * 5 + 5 * 4x^2 + 5 * 5 = 8x^3y + 10xy + 20x^2 + 25 b) (6xy+4)(2x^2+1): = 6xy * 2x^2 + 6xy * 1 + 4 * 2x^2 + 4 * 1 = 12x^3y + 6xy + 8x^2 + 4 c) (9x^2+4)(3x+5): = 9x^2 * 3x + 9x^2 * 5 + 4 * 3x + 4 * 5 = 27x^3 + 45x^2 + 12x + 20 d) (-2xy+6)(1/2xy+7): = -2xy * 1/2xy + (-2xy) * 7 + 6 * 1/2xy + 6 * 7 = -xy + (-14xy) + 3 + 42 = -15xy + 45 e) (4x+1)(2x^2+5x+2): = 4x * 2x^2 + 4x * 5x + 4x * 2 + 1 * 2x^2 + 1 * 5x + 1 * 2 = 8x^3 + 20x^2 + 8x + 2x^2 + 5x + 2 = 8x^3 + 22x^2 + 13x + 2 f) (2x^2y+3x)(2x+1): = 2x^2y * 2x + 2x^2y * 1 + 3x * 2x + 3x * 1 = 4x^3y + 2x^2y + 6x^2 + 3x g) (4xy+5x^2y)(2xy+6): = 4xy * 2xy + 4xy * 6 + 5x^2y * 2xy + 5x^2y * 6 = 8x^2y^2 + 24xy + 10x^3y + 30x^2y = 8x^2y^2 + 30x^2y + 24xy h) (-1/2x^2+6)(4xy+5): = -1/2x^2 * 4xy + (-1/2x^2) * 5 + 6 * 4xy + 6 * 5 = -2xy + (-5/2x^2) + 24xy + 30 = 22xy + (-5/2x^2) + 30