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a)
\(A=\left(x+3\right)\left(x^2-3x+9\right)-\left(54+x^3\right)\)
\(=x^3-3x^2+9x+3x^2-9x+27-54-x^3\)
\(=-27\)
or
\(A=x^3+27-54-x^3=-27\)
b)
\(B=\left(2x+y\right)\left(4x^2-2xy+y^2\right)-\left(2x-y\right)\left(4x^2+2xy+y^2\right)\)
\(=8x^3+y^3-8x^3+y^3=2y^3\)
c)
\(C=\left(2x+1\right)^2+\left(1-3x\right)^2+2\left(2x+1\right)\left(3x-1\right)\)
\(=\left(2x+1+3x-1\right)^2=\left(5x\right)^2=25x^2\)
d)
\(D=\left(x-2\right)\left(x^2+2x+4\right)-\left(x+1\right)^3+3\left(x-1\right)\left(x+1\right)\)
\(=x^3-8-\left(x-1\right)^3+3\left(x-1\right)\left(x+1\right)\)
\(=6x^2-3x-10\)
\(a,\left(3x+5\right)^2+\left(3x-5\right)^2-\left(3x+2\right)\left(3x-2\right)=9x^2+30x+25+9x^2-30x+25-9x^2+4=9x^2+54\)
\(b,BT=2x\left(4x^2-4x+1\right)-3x\left(x^2-9\right)-4x\left(x^2+2x+1\right)=8x^3-8x^2+2x-3x^3+27x-4x^3-8x^2-4x=x^3-16x^2+25x\)
\(c,BT=\left(x+y-z\right)^2-2\left(x+y-z\right)\left(x+y\right)+\left(x+y\right)^2=\left(x+y-z-x-y\right)^2=z^2\)
a ) \(A=\frac{ax^2\left(a-x\right)-a^2x\left(x-a\right)}{3a^2-3x^2}=\frac{ax\left(a-x\right)\left(a+x\right)}{3\left(a-x\right)\left(a+x\right)}=\frac{ax}{3}\)
Thay \(a=\frac{1}{2};x=-3\), ta có :
\(A=\frac{\frac{1}{2}.-3}{3}=-\frac{1}{2}\)
b ) \(B=\frac{\left(ab+bc+cd+da\right)abcd}{\left(c+d\right)\left(a+b\right)+\left(b-c\right)\left(a-d\right)}=\frac{\left[\left(ab+ad\right)+\left(bc+cd\right)\right]abcd}{ca+cb+da+db+ba-bd-ca+cd}\)
\(=\frac{\left[a\left(b+d\right)+c\left(b+d\right)\right]abcd}{ba+da+cb+cd}=\frac{\left(b+d\right)\left(a+c\right)abcd}{\left(b+d\right)\left(a+c\right)}=abcd\)
Thay \(a=-3;b=-4;c=2;d=3\), ta có :
\(B=\left(-3\right).\left(-4\right).2.3=72\)
a, +) Xét \(x\ge0\)
\(\Rightarrow A=x+x=2x\)
+) Xét x < 0
\(\Rightarrow A=x+\left(-x\right)=0\)
Vậy...
b, +) Xét \(x\ge0\) có:
\(B=x-x=0\)
+) Xét x < 0 có:
\(B=-x-x=-2x\)
Vậy..
c, \(C=2\left(3x-1\right)-\left|5-x\right|=6x-2-\left|5-x\right|\)
+) Xét \(x\le5\) ta có:
\(C=6x-2-5+x=7x-7\)
+) Xét x > 5 ta có:
\(C=6x-2-x+5=5x+3\)
Vậy...
d, \(D=2\left(2x-1\right)-3\left|2x+3\right|=4x-2-\left|6x+9\right|\)
+) Xét \(x\ge\dfrac{-3}{2}\) có:
\(D=4x-2-6x-9=-2x-11\)
+) Xét \(x< \dfrac{-3}{2}\) ta có:
\(D=4x-2+6x+9=10x+7\)
Vậy...
a: =x^2-4-(x^2-2x-3)
=x^2-4-x^2+2x+3
=2x-1
b: \(=2x^2+3x-10x-15-2x^2+6x+x+7\)
=-8
c: \(=a^2+2ab+b^2-a^2+2ab-b^2=4ab\)
Nếu x < 1 => |-x + 1| = -x + 1
|2x - 3| = -(2x - 3) = -2x + 3
Khi đó B = |-x + 1| + |2x - 3| - 2(x - 1)
= -x + 1 - 2x + 3 - 2x + 2
= - 5x + 6
Nếu \(1\le x\le1,5\)
=> |-x + 1| = x - 1
|2x - 3| = --2x + 3
Khi đó B = x - 1 - 2x + 3 - 2x + 2
= -4x + 4
Nếu x > 1,5 => |-x + 1| = x - 1
|2x - 3| = 2x - 3
Khi đó B = x - 1 + 2x - 3 -2x + 2
= x - 2
how to đăng bài?
please help me