rút gọn biểu thức :
\(\left(x-3\right)\left(x+5\right)-\left(x-2\right)\left(x+2\right)\left(x-2\right)^2+\left(x+3\right)^2-2\left(x-1\right)\left(x+1\right)\)
help me !! cần gấp ,ai đúng mik tick , c.ơn mn nhìu
Rút gọn các biểu thức sau:
a/ \(\left(x-2y^{ }\right)^2+\left(x-\dfrac{1}{2}y\right)\left(x+\dfrac{1}{2}y\right)\)
b/ \(\left(x-2\right)^2+\left(x+3\right)^2-2\left(x-1\right)\left(x+1\right)\)
a: \(\left(x-2y\right)^2+\left(x-\dfrac{1}{2}y\right)\left(x+\dfrac{1}{2}y\right)\)
\(=x^2-4xy+4y^2+x^2-\dfrac{1}{4}y^2\)
\(=2x^2-4xy+\dfrac{15}{4}y^2\)
b: \(\left(x-2\right)^2+\left(x+3\right)^2-2\left(x-1\right)\left(x+1\right)\)
\(=x^2-4x+4+x^2+6x+9-2\left(x^2-1\right)\)
\(=2x^2+2x+13-2x^2+2\)
=2x+15
a) \(=x^2-4xy+4y^2+x^2-\dfrac{1}{4}y^2=2x^2-4xy+\dfrac{15}{4}y^2\)
b) \(=x^2-4x+4+x^2+6x+9-2x^2+2\)
\(=2x+15\)
a; \(\left(x-2y\right)^2+\left(x-\dfrac{1}{2}y\right)\left(x+\dfrac{1}{2}y\right)\)
= \(x^2-4xy+4y^2+x^2-\dfrac{1}{4}y^2\)
= \(2x^2-4xy+\dfrac{15}{4}y^2\)
b; \(\left(x-2\right)^2+\left(x+3\right)^2-2\left(x-1\right)\left(x+1\right)\)
= \(x^2-4x+4+x^2+6x+9-2x^2+2\)
= \(2x+15\)
Rút gọn các biểu thức sau :
a ) A = \(\left(\frac{1}{4}x-y\right)\left(x^2+4xy+16y^2\right)+4\left(4y^3-\frac{1}{16}x^3+1\right)\)
b ) B = \(2x\left(x-4\right)^2-\left(x+5\right)\left(x-2\right)\left(x+2\right)+2\left(x-5\right)^2-\left(x-1\right)^2\)
c ) C = \(\frac{80x^3-125x}{3\left(x-3\right)-\left(x-3\right)\left(8-4x\right)}\)
d ) D = \(\frac{\left(a-b\right)\left(c-d\right)}{\left(b^2-a^2\right)\left(d^2-c^2\right)}\)
Mình đg cần gấp . đảm bảo tick trả đầy đủ
a) \(A=\left(\frac{1}{4}x-y\right)\left(x^2+4xy+16y^2\right)+4\left(4y^3-\frac{1}{16}x^3+1\right)\)
\(\Leftrightarrow A=\frac{1}{4}\left(x-4y\right)\left(x^2+4xy+16y^2\right)+16y^3-\frac{1}{4}x^3+4\)
\(\Leftrightarrow A=\frac{1}{4}\left(x^3-64y^3\right)+16y^3-\frac{1}{4}x^3+4\)
\(\Leftrightarrow A=\frac{1}{4}x^3-16y^3+16y^3-\frac{1}{4}x^3+4\)
\(\Leftrightarrow A=4\)
b) \(B=2x\left(x-4\right)^2-\left(x+5\right)\left(x-2\right)\left(x+2\right)+2\left(x-5\right)^2-\left(x-1\right)^2\)
\(\Leftrightarrow B=2x\left(x^2-8x+16\right)-\left(x+5\right)\left(x^2-4\right)+2\left(x^2-10x+25\right)-\left(x^2-2x+1\right)\)
\(\Leftrightarrow B=2x^3-16x^2+32x-x^3-5x^2+4x+20+2x^2-20x+50-x^2+2x-1\)
\(\Leftrightarrow B=x^3-20x^2+18x+69\)
c) \(C=\frac{80x^3-125x}{3\left(x-3\right)-\left(x-3\right)\left(8-4x\right)}\)
\(\Leftrightarrow C=\frac{5x\left(16x^2-25\right)}{\left(x-3\right)\left(3-8+4x\right)}\)
\(\Leftrightarrow C=\frac{5x\left(4x-5\right)\left(4x+5\right)}{\left(x-3\right)\left(4x-5\right)}\)
\(\Leftrightarrow C=\frac{5x\left(4x+5\right)}{x-3}\)
\(\Leftrightarrow C=\frac{20x^2+25x}{x-3}\)
d) \(D=\frac{\left(a-b\right)\left(c-d\right)}{\left(b^2-a^2\right)\left(d^2-c^2\right)}\)
\(\Leftrightarrow D=\frac{\left(a-b\right)\left(c-d\right)}{\left(a^2-b^2\right)\left(c^2-d^2\right)}\)
\(\Leftrightarrow D=\frac{\left(a-b\right)\left(c-d\right)}{\left(a-b\right)\left(a+b\right)\left(c-d\right)\left(c+d\right)}\)
\(\Leftrightarrow D=\frac{1}{\left(a+b\right)\left(c+d\right)}\)
Chúc bạn học tốt !
Rút gọn các biểu thức sau:
a/\(\left(x+\dfrac{1}{3}x+\dfrac{1}{9}\right)\left(x-\dfrac{1}{3}\right)-\left(x-\dfrac{1}{3^{ }}\right)^2\)
b/\(\left(x_{ }^2-2\right)^3-x\left(x+1\right)\left(x-1\right)+x\left(x-3\right)\)
MẤY BẠN GIÚP MK VS Ạ AI NHANH MK VOTE NHA
a) \(=x^3-\dfrac{1}{27}-x^2+\dfrac{2}{3}x-\dfrac{1}{9}=x^3-x^2+\dfrac{2}{3}x-\dfrac{2}{27}\)
b) \(=x^6-6x^4+12x^2-8-x^3+x+x^2-3x=x^6-6x^4-x^3+13x^2-2x-8\)
Rút gọn biểu thức sau:
a, \(\left(x-2\right)\left(x^2+2x+4\right)-\left(x+1\right)^2+3\left(x-1\right)\left(x+1\right)\)
b, \(\left(x^4-5x^2+25\right)\left(x^2+5\right)-\left(2+x^2\right)^2+3\left(1+x^2\right)^2\)
Rút gọn các biểu thức sau:
A= \(3\left(x+2\sqrt{x}\right)-\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\)
B= \(\left(\sqrt{x}+1\right)\left(\sqrt{x}+3\right)-2\left(\sqrt{x}-1\right)^2\)
C= \(3x-3\sqrt{x}-2+\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\)
D= \(\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)-\left(2\sqrt{x}+1\right)\left(\sqrt{x}-2\right)\)
E= \(\left(\sqrt{x}+4\right)\left(\sqrt{x}-4\right)-\left(2\sqrt{x}-1\right)\left(\sqrt{x}+2\right)\)
\(A=3\left(x+2\sqrt{x}\right)-\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\)
\(=3x+6\sqrt{x}-\left(x-1\right)\)
\(=3x+6\sqrt{x}-x+1\)
\(=2x+6\sqrt{x}+1\)
\(B=\left(\sqrt{x}+1\right)\left(\sqrt{x}+3\right)-2\left(\sqrt{x}-1\right)^2\)
\(=x+3\sqrt{x}+\sqrt{x}+3-2\left(x-2\sqrt{x}+1\right)\)
\(=x+4\sqrt{x}+3-2x+4\sqrt{x}-2\)
\(=-x+8\sqrt{x}+1\)
\(C=3x-3\sqrt{x}-2+\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\)
\(=3x-3\sqrt{x}-2+\left(\sqrt{x^2}-1\right)\)
\(=3x-3\sqrt{x}-2+x-1\)
\(=4x-3\sqrt{x}-3\)
\(D=\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)-\left(2\sqrt{x}+1\right)\left(\sqrt{x}-2\right)\)
\(=x-9-\left(2x-3\sqrt{x}-2\right)\)
\(=x-9-2x+3\sqrt{x}+2\)
\(=-x+3\sqrt{x}-7\)
\(E=\left(\sqrt{x}+4\right)\left(\sqrt{x}-4\right)-2\left(2\sqrt{x}-1\right)\left(\sqrt{x}+2\right)\)
\(=\sqrt{x^2}-2^2-2\left(2x+4\sqrt{x}-\sqrt{x}-2\right)\)
\(=x-4-2\left(2x+3\sqrt{x}-2\right)\)
\(=x-4-4x-6\sqrt{x}+4\)
\(=-3-6\sqrt{x}\)
Rút gọn biểu thức sau
A=\(\dfrac{1}{x-1}\sqrt{75\left(x-1\right)^3}\left(x>1\right)
\)
B=\(5\sqrt{4x}-3\sqrt{\dfrac{100x}{9}}-\dfrac{4}{x}\sqrt{\dfrac{x^3}{4}}\left(x>0\right)
\)
C=\(x-4+\sqrt{16-8x+x^2}\left(x>4\right)\)
Help me
a: \(A=\dfrac{1}{x-1}\cdot5\sqrt{3}\cdot\left|x-1\right|\cdot\sqrt{x-1}\)
\(=\dfrac{5\sqrt{3}}{x-1}\cdot\left(x-1\right)\cdot\sqrt{x-1}=5\sqrt{3}\cdot\sqrt{x-1}\)
b: \(B=10\sqrt{x}-3\cdot\dfrac{10\sqrt{x}}{3}-\dfrac{4}{x}\cdot\dfrac{x\sqrt{x}}{2}\)
\(=10\sqrt{x}-10\sqrt{x}-\dfrac{4\sqrt{x}}{2}=-2\sqrt{x}\)
c: \(C=x-4+\left|x-4\right|\)
=x-4+x-4
=2x-8
Rút gọn các biểu thức sau:
A= \(\left(x+1\right).\left(x^2-x+1\right)+2.\left(x+1\right)-x.\left(x^2+2\right).\)
B= \(\left(5x+1\right).\left(x+7\right)-5x.\left(x-1\right).\)
A=x3+1+2x+2-x3-2x=3
B=5x2+36x+7-5x2+5x=41x+7
\(\left(x^2_{ }+1\right)\left(x-3\right)-\left(x-3\right)\left(x^2-1\right)\)
rút gọn biểu thức
\(=\left(x-3\right)\left(x^2+1-x^2+1\right)=2\left(x-3\right)\)
(x2 + 1)(x - 3) - (x - 3)(x2 - 1)
= [x2 + 1 - (x2 - 1)](x - 3)
= (x2 + 1 - x2 + 1)(x - 3)
= 2(x - 3)
`=(x-3)[x^2+1-(x^2-1)]`
`=(x-3)(x^2+1-x^2+1)`
`=2(x-3)`
Bài 4:Rút gọn biểu thức
a) \(2x\left(x-5\right)-\left(x-2\right)^2-\left(x+3\right).\left(x-3\right)\)
b) \(\left(x+1\right)^2+3\left(x-5\right).\left(x+5\right)-\left(2x-1\right)^2\)
c) \(2x\left(x-7\right)-\left(x+3\right)\left(x-2\right)-\left(x+4\right)\left(x-4\right)\)
d) \(\left(x+3\right)\left(x-3\right)-\left(x+5\right).\left(x-1\right)-\left(x-4\right)^2\)
a. \(2x\left(x-5\right)-\left(x-2\right)^2-\left(x+3\right)\left(x-3\right)\)
\(=2x^2-10x-x^2+4x-4-x^2+9\)
\(=-6x+5\)
b. \(\left(x+1\right)^2+3\left(x-5\right)\left(x+5\right)-\left(2x-1\right)^2\)
\(=x^2+2x+1+3x^2-75-4x^2+4x-1\)
\(=6x-75\)
c. \(2x\left(x-7\right)-\left(x+3\right)\left(x-2\right)-\left(x+4\right)\left(x-4\right)\)
\(=2x^2-14x-x^2-x+6-x^2+16\)
\(=-15x+22\)
d. \(\left(x+3\right)\left(x-3\right)-\left(x+5\right)\left(x-1\right)-\left(x-4\right)^2\)
\(=x^2-9-x^2-4x+5-x^2+8x-16\)
\(=-x^2+4x-20\)
Bài làm:
a) \(2x\left(x-5\right)-\left(x-2\right)^2-\left(x+3\right)\left(x-3\right)\)
\(=2x^2-10x-x^2+4x-4-x^2+9\)
\(=-6x+5\)
b) \(\left(x+1\right)^2+3\left(x-5\right)\left(x+5\right)-\left(2x-1\right)^2\)
\(=x^2+2x+1+3x^2-75-4x^2+4x-1\)
\(=6x-75\)
c) \(2x\left(x-7\right)-\left(x+3\right)\left(x-2\right)-\left(x+4\right)\left(x-4\right)\)
\(=2x^2-14x-x^2-x+6-x^2+16\)
\(=-15x+22\)
d) \(\left(x+3\right)\left(x-3\right)-\left(x+5\right)\left(x-1\right)-\left(x-4\right)^2\)
\(=x^2-9-x^2-4x+5-x^2+8x-16\)
\(=-x^2-4x-20\)
đầy đủ từng bước nhé
\(a,2x\left(x-5\right)-\left(x-2\right)^2-\left(x+3\right)\left(x-3\right)\)
\(=2x^2-10x-\left(x^2-4x+4\right)-\left(x^2-9\right)\)
\(=2x^2-10x-x^2+4x-4-x^2+9\)
\(=\left(2x^2-x^2-x^2\right)+\left(4x-10x\right)+\left(9-4\right)\)
\(=0-6x+5=5-6x\)
\(b,\left(x+1\right)^2+3\left(x-5\right)\left(x+5\right)-\left(2x-1\right)^2\)
\(=\left(x^2+2x+1\right)+3\left(x^2-25\right)-\left(4x^2-4x+1\right)\)
\(=x^2+2x+1+3x^2-75-4x^2+4x-1\)
\(=\left(x^2+3x^2-4x^2\right)+\left(2x+4x\right)+\left(1-1-75\right)\)\(=6x-75\)
\(c,2x\left(x-7\right)-\left(x+3\right)\left(x-2\right)-\left(x+4\right)\left(x-4\right)\)
\(=2x^2-14x-\left(x+2\right)\left(x-2\right)-x+2-\left(x+4\right)\left(x-4\right)\)
\(=2x^2-14x-x^2+4-x+2-x^2+16\)
\(=\left(2x^2-x^2-x^2\right)+\left(-14x-x\right)+\left(16+2+4\right)\)
\(=0-15x+22=22-15x\)
\(d,\left(x+3\right)\left(x-3\right)-\left(x+5\right)\left(x-1\right)-\left(x-4\right)^2\)
\(=\left(x+3\right)\left(x-3\right)-\left(x+1\right)\left(x-1\right)-4\left(x-1\right)-\left(x-4\right)^2\)
\(=x^2-9-x^2+1-4x+4-\left(x^2-8x+16\right)\)
\(=\left(x^2-x^2\right)-4x+\left(4+1-9\right)-x^2+8x-16\)
\(=-4x-4-x^2+8x-16=-x^2+\left(8x-4x\right)-\left(16+4\right)\)
\(=-x^2+4x-20\)