Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
a;
M + (5\(x^2\) - 2\(xy\)) = 8\(x^2\) - 7\(xy\) - 5y\(^2\)
M = 8\(x^2\) - 7\(xy\) - 5y\(^2\) -(5\(x^2\) - 2\(xy\))
M = 8\(x^2\) - 7\(xy\) - 5y\(^2\) - 5\(x^2\) + 2\(xy\)
M = (8\(x^2\) - 5\(x^2\)) - (7\(xy\) - 2\(xy\)) - 5y\(^2\)
M = 3\(x^2\) - 5\(xy\) - 5y\(^2\)
Câu b:
(15\(xy\) - 3\(x^2y\) + 1) - M = 2\(x^2y\) - 15\(xy\) + \(x-2\)
M = (15\(xy\) - 3\(x^2y\) + 1) - (2\(x^2y\) - 15\(xy\) + \(x-2\))
M = 15\(xy\) - 3\(x^2y\) + 1- 2\(x^2y\) + 15\(xy\) - \(x+2\)
M = -(3\(x^2y\) + 2\(x^2y\)) + (15\(xy\) + 15\(xy\)) - \(x\) + (1+ 2)
M = - 5\(x^2y\) + 30\(xy\) - \(x\) + 3
a)
+) Nếu x > 0 thì A = x + x = 2x
+) Nếu x = 0 thì A = 0 + 0 = 0
+) Nếu x < 0 thì A = -x + x = 0
b) B = 2 ( 3x - 1 ) - | 5 - x |
B = 6x - 2 - | 5 - x |
Xét 3 t/h như câu a)
a)+) Nếu x > 0 thì A = x + x = 2x
+) Nếu x = 0 thì A = 0 + 0 = 0
+) Nếu x < 0 thì A = -x + x = 0
b) B = 2 ( 3x - 1 ) - | 5 - x |
B = 6x - 2 - | 5 - x |
Xét 3 t/h như câu a)
bài 1
a) \(-\frac{1}{3}xy\).(3\(x^2yz^2\))
=\(\left(-\frac{1}{3}.3\right)\).\(\left(x.x^2\right)\).(y.y).\(z^2\)
=\(-x^3\).\(y^2z^2\)
b)-54\(y^2\).b.x
=(-54.b).\(y^2x\)
=-54b\(y^2x\)
c) -2.\(x^2y.\left(\frac{1}{2}\right)^2.x.\left(y^2.x\right)^3\)
=\(-2x^2y.\frac{1}{4}.x.y^6.x^3\)
=\(\left(-2.\frac{1}{4}\right).\left(x^2.x.x^3\right).\left(y.y^2\right)\)
=\(\frac{-1}{2}x^6y^3\)
Bài 3:
a) \(f\left(x\right)=-15x^2+5x^4-4x^2+8x^2-9x^3-x^4+15-7x^3\)
\(f\left(x\right)=\left(5x^4-x^4\right)-\left(9x^3+7x^3\right)-\left(15x^2+4x^2-8x^2\right)+15\)
\(f\left(x\right)=4x^4-16x^3-11x^2+15\)
b)
\(f\left(x\right)=4x^4-16x^3-11x^2+15\)
\(f\left(1\right)=4\cdot1^4-16\cdot1^3-11\cdot1^2+15\)
\(f\left(1\right)=4\cdot1^4-16\cdot1^3-11\cdot1^2+15\)
\(f\left(1\right)=-8\)
\(f\left(x\right)=4x^4-16x^3-11x^2+15\)
\(f\left(-1\right)=4\cdot\left(-1\right)^4-16\cdot\left(-1\right)^3-11\cdot\left(-1\right)^2+15\)
\(f\left(-1\right)=24\)
\(\left\{{}\begin{matrix}f\left(x\right)=3x^4+5yx^2-3yx+y^4+z^2\\M\left(x\right)=ax^4+bx^2+cx+D\end{matrix}\right.\)
\(f\left(x\right)+M\left(x\right)=\left(3+a\right)x^4+\left(5y+a\right)x^2+\left(-3y+c\right)x+y^4+z^2+D\)\(\Leftrightarrow\left\{{}\begin{matrix}a=-3\\b=-5y\\c=3y\end{matrix}\right.\)\(\Rightarrow M\left(x\right)=-3x^4-5yx^2+3yx+y^4+z^2+D\) với D tùy ý không chứa x
\(\int f\left(x\right)dx=x^3+C\)
\(\sum a\left(b^2-1\right)\left(c^2-1\right)\)
\(a\left(b^2-1\right)\left(c^2-1\right)+b\left(a^2-1\right)\left(c^2-1\right)+c\left(b^2-1\right)\left(a^2-1\right)\)
\(\begin{matrix}\sum a\left(b^2-1\right)\left(c^2-1\right)=\sum\left(ab^2-a\right)\left(c^2-1\right)=\sum\left(ab^2c^2-ab^2-ac^2+a\right)\\\left(ab^2c^2-ab^2-ac^2+a\right)+\\\left(a^2bc^2-ba^2-bc^2+b\right)+\\\left(a^2b^2c-b^2c-a^2c+c\right)\end{matrix}\)
\(a+b+c\Rightarrow a+b=abc-c\) \(\Rightarrow\sum ab\left(a+b\right)=\sum ab\left(abc-c\right)=\sum a^2b^2c-abc\)
\(\left[abc\left(bc+ac+ab\right)\right]-\left[ab\left(a+b\right)+ac\left(a+c\right)+bc\left(b+c\right)\right]+\left[\left(a+b+c\right)\right]\)
\(\sum a^2b^2c-abc=\left(-abc+a^2b^2c\right)+\left(-abc+a^2bc^2\right)+\left(-abc+ab^2c^2\right)=-3abc+abc\left(ab+bc+ac\right)\)
\(\left[abc\left(bc+ac+ab\right)\right]+3abc-abc\left(ab+bc+ac\right)+\left(a+b+c\right)=3abc+abc=4abc=VP\)
a: \(M+N-P=2a^2-3a+1+5a^2+a-a^2+4=6a^2-2a+5\)
b: \(=2y-x-\left\{2x-y-\left[3x+y-5y+x\right]\right\}\)
\(=2y-x-\left\{2x-y-\left[4x-4y\right]\right\}\)
\(=2y-x-\left\{2x-y-4x+4y\right\}\)
\(=2y-x-\left[-2x+3y\right]\)
\(=-x+2y+2x-3y=x-y=\left(a-b\right)^2-\left(a-b\right)^2\)
=4ab
c: TH1: x>=1/2
A=5x-3-2x+1=3x-2
TH2: x<1/2
A=5x-3+2x-1=7x-4
1a) \(10^{n+1}-6\cdot10^n\)
\(=10^n\cdot10-6\cdot10^n\)
= \(10^n\left(10-6\right)\)
\(=10^n\cdot4\)
b) \(2^{n+3}+2^{n+2}-2^{n+1}+2^n\)
\(=2^n\cdot2^3+2^n\cdot2^2-2^n\cdot2+2^n\)
\(=2^n\left(2^3+2^2-2+1\right)\)
\(=2^n\cdot11\)
c) \(90\cdot10^k-10^{k+2}+10^{k+1}\)
\(=90\cdot10^k-10^k\cdot10^2+10^k\cdot10\)
\(=10^k\left(90-10^2+10\right)=0\)
d) \(2,5\cdot5^{n-3}\cdot10+5^n-6\cdot5^{n-1}\)
\(=\dfrac{2,5\cdot10\cdot5^n}{5^3}+5^n-\dfrac{6\cdot5^n}{5}\)
\(=\dfrac{5^n}{5}+5^n-\dfrac{6\cdot5^n}{5}\)
\(=\dfrac{5^n+5^n\cdot5-6\cdot5^n}{5}=\dfrac{5^n\left(5-6\right)+5^n}{5}=0\)
2. \(M+\left(6x^2-4xy\right)=7x^2-8xy+y^2\)
\(M=\left(7x^2-8xy+y^2\right)-\left(6x^2-4xy\right)\)
\(M=7x^2-8xy+y^2-6x^2+4xy\)
\(M=7x^2-6x^2-8xy+4xy+y^2\)
\(M=x^2-4xy+y^2\)
TH1: \(x\ge\frac{-1}{3}\)
\(\Rightarrow3x+1-x-2=2x-1\)
TH2: \(x< \frac{-1}{3}\)
\(\Rightarrow-3x-1-x-2=-4x-3\)
Nhớ tick
\(A=\left|3x+1\right|-x-2\)
Với \(x\ge\frac{1}{3}\)
\(\Rightarrow3x+1-x-2\)
\(=\left(3x-x\right)+\left(1-2\right)\)
\(=2x-1.\)
Với \(x< -\frac{1}{3}\)
\(\Rightarrow-3x-1-x-2\)
\(=\left(-3x-x\right)+\left(-1-2\right)\)
\(=-4x-3.\)
Chúc bạn học tốt!