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tớ lm câu a thui nha , tại khó quá ^^
a/ \(=3x^6+3x^5+6x^4+3x^3+3x^2-7x^5-7x^4-14x^3-7x^2-7x+3x^4+3x^3+6x^2+3x+1\)
\(=3x^2\left(x^4+x^3+2x^2+x+1\right)-7x\left(x^4+x^3+2x^2+x+1\right)+3\left(x^4+x^3+2x^2+x+1\right)\)
\(=\left(3x^2-7x+3\right)\left(x^4+x^3+x^2+x^2+x+1\right)\)
\(=\left(3x^2-7x+3\right)\left[x^2\left(x^2+x+1\right)+\left(x^2+x+1\right)\right]\)
\(=\left(3x^2-7x+3\right)\left(x^2+1\right)\left(x^2+x+1\right)\)
\(x^2-2x-4y^2-4y\)
\(=\left(x^2-4y^2\right)-\left(2x+4y\right)\)
\(=\left(x-2y\right)\left(x+2y\right)-2\left(x+2y\right)\)
\(=\left(x+2y\right)\left(x-2y-2\right)\)
\begin{array}{l} a){\left( {ab - 1} \right)^2} + {\left( {a + b} \right)^2}\\ = {a^2}{b^2} - 2ab + 1 + {a^2} + 2ab + {b^2}\\ = {a^2}{b^2} + 1 + {a^2} + {b^2}\\ = {a^2}\left( {{b^2} + 1} \right) + \left( {{b^2} + 1} \right)\\ = \left( {{a^2} + 1} \right)\left( {{b^2} + 1} \right)\\ c){x^3} - 4{x^2} + 12x - 27\\ = {x^3} - 27 + \left( { - 4{x^2} + 12x} \right)\\ = \left( {x - 3} \right)\left( {{x^2} + 3x + 9} \right) - 4x\left( {x - 3} \right)\\ = \left( {x - 3} \right)\left( {{x^2} + 3x + 9 - 4x} \right)\\ = \left( {x - 3} \right)\left( {{x^2} - x + 9} \right)\\ b){x^3} + 2{x^2} + 2x + 1\\ = {x^3} + 2{x^2} + x + x + 1\\ = x\left( {{x^2} + 2x + 1} \right) + \left( {x + 1} \right)\\ = x{\left( {x + 1} \right)^2} + \left( {x + 1} \right)\\ = \left( {x + 1} \right)\left( {x\left( {x + 1} \right) + 1} \right)\\ = \left( {x + 1} \right)\left( {{x^2} + x + 1} \right)\\ d){x^4} - 2{x^3} + 2x - 1\\ = {x^4} - 2{x^3} + {x^2} - {x^2} + 2x - 1\\ = {x^2}\left( {{x^2} - 2x + 1} \right) - \left( {{x^2} - 2x + 1} \right)\\ = \left( {{x^2} - 2x + 1} \right)\left( {{x^2} - 1} \right)\\ = {\left( {x - 1} \right)^2}\left( {x - 1} \right)\left( {x + 1} \right)\\ = {\left( {x - 1} \right)^3}\left( {x + 1} \right)\\ e){x^4} + 2{x^3} + 2{x^2} + 2x + 1\\ = {x^4} + 2{x^3} + {x^2} + {x^2} + 2x + 1\\ = {x^2}\left( {{x^2} + 2x + 1} \right) + \left( {{x^2} + 2x + 1} \right)\\ = \left( {{x^2} + 2x + 1} \right)\left( {{x^2} + 1} \right)\\ = {\left( {x + 1} \right)^2}\left( {{x^2} + 1} \right) \end{array} |
A) 1/2 x(x^2-4)+4(x+2)
=1/2x(x-2)(x+2)+4(x+2)
=(x+2)(1/2x^2-x+4)
b) 21(x-y)^2-7(x-y)^3
= (x-y)^2(21-7x+7y)
=(x-y)^2.7(3-x+y)
c) 1/8x^3-3/4x^2+3/2x-1
=(1/2x)^3-3.(1/2x)^2.1+3.1/2x.1^2-1
=(1/2x-1)^3
a) 2x3 + 8x2 - 8x
= 2x(x2 + 4x - 4)
= 2x(x2 + 4x + 4 - 8)
= 2x[(x + 2)2 - 8]
= \(2x\left(x+2-\sqrt{8}\right)\left(x+2+\sqrt{8}\right)\)
b) a2 - b2 + 4a + 4b
= (a - b)(a + b) + 4(a + b)
= (a + b)(a - b + 4)
c) x2 - 2x - 3
= x2 + x - 3x - 3
= x(x + 1) - 3(x + 1)
= (x + 1)(x - 3)
d) x2 - 4x - 3
= x2 - 4x + 4 - 7
= (x + 2)2 - 7
= \(\left(x+2-\sqrt{7}\right)\left(x+2+\sqrt{7}\right)\)
a) co sai de ko
b)x3-2x2+4x2-8x+3x-6=x2(x-2)+4x(x-2)+3(x-2)=(x-2)(x2+4x+3)=(x-2)(x+3)(x+1)
c)x3-2x2+2x2-4x-3x+6=x2(x-2)+2x(x-2)-3(x-2)=(x-2)(x2+2x-3)=(x-2)(x+3)(x-1)
d)x3-3x2+x2-3x-2x+6=x2(x-3)+x(x-3)-2(x-3)=(x-3)(x2+x-2)=(x-3)(x+2)(x-1)
b)3x^2-18x+27=3x^2-9x-9x+27=3x*(x-3)-9*(x-3)=(x-3)*(3x-9)=(x-3)*3*(x-3)=3*(x-3)^2
c)x^3-4x^2-12x+27=(x+3)*(x^2-3x+9-4)=(x+3)*(x^2-3x+5)
d)27x^3-1/27=(3x-1/3)*(9x^2-x+1/9) (hang dt)
con a) voi e) mk chiu
a/ \(x^3-5x^2+8x-4\)
= \(\left(x^3-x^2\right)-\left(4x^2-4x\right)+\left(4x-4\right)\)
= \(x^2\left(x-1\right)-4x\left(x-1\right)+4\left(x-1\right)\)
= \(\left(x-1\right)\left(x^2-4x+4\right)\)
= \(\left(x-1\right)\left(x-2\right)^2\)
b/ \(x^3-x^2+x-1\)
= \(\left(x^3-x^2\right)+\left(x-1\right)\)
= \(x^2\left(x-1\right)+\left(x-1\right)\)
= \(\left(x-1\right)\left(x^2+1\right)\)
\(A=x^3+4x^2-8x-8=\left(x^3-8\right)+4x\left(x-2\right)=\left(x^3-2^3\right)+4x\left(x-2\right)\)
\(=\left(x-2\right)\left(x^2+2x+4\right)+4x\left(x-2\right)=\left(x-2\right)\left(x^2+2x+4+4x\right)=\left(x-2\right)\left(x^2+6x+4\right)\)
\(B=a^2+b^2-a^2b^2+ab-a-b=\left(ab-a\right)-\left(a^2b^2-a^2\right)+\left(b^2-b\right)\)
\(=a\left(b-1\right)-a^2\left(b^2-1\right)+b\left(b-1\right)=a\left(b-1\right)-a^2\left(b-1\right)\left(b+1\right)+b\left(b-1\right)\)
\(=\left(b-1\right)\left(a-a^2b-a^2+b\right)\)
\(C=x^4-x^3-x+1=x^3\left(x-1\right)-\left(x-1\right)=\left(x-1\right)\left(x^3-1\right)\)
Đoàn Thị Huyền Đoan: Hình như câu A bạn chép xuống bị sai đề rồi!
a)\(2x^2+8x+8\)
\(\Leftrightarrow2\left(x^2+4x+4\right)\)
\(\Leftrightarrow2\left(x+2\right)^2\)
P/s tham khảo nha
b)\(y^2-x^2+2y+1\)
\(\Leftrightarrow\left(y+1\right)^2-x^2\)
\(\Leftrightarrow\left(y+1-x\right)\left(y+1+x\right)\)
P/s tham khảo nha
a, \(x^3+8-4x^2-8x\)
\(=x^3+2x^2-6x^2-12x+4x+8\)
\(=x^2\left(x+2\right)-6x\left(x+2\right)+4\left(x+2\right)\)
\(=\left(x+2\right)\left(x^2-6x+4\right)\)
b, \(x^2+2x+1-y^2\)
\(=\left(x+1\right)^2-y^2=\left(x+1-y\right)\left(x+1+y\right)\)
c, \(x^3-64\)
\(=x^3-4^3=\left(x-4\right)\left(x^2+4x+16\right)\)
Chúc bạn học tốt!!!
A)
\(x^3+8-4x^2-8x=\left(x+2\right)\left(x^2-2x+4\right)-4x\left(x+2\right)\\ \left(x+2\right)\left(x^2-6x+4\right)\)
B)
\(x^2+2x+1-y^2=\left(x+1\right)^2-y^2\\ =\left(x+1+y\right)\left(x+1-y\right)\)
C)
\(x^3-64=x^3-4^3\\ \left(x-4\right)\left(x^2+4x+16\right)\)