a) \(4x^4+1\)
b) \(4x^4+81\)
c) \(64x^4+y^4\)
d) \(x^8+4\)
e) \(x^4+x^2+1\)
f) \(x^7+x^5+1\)
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Những câu hỏi liên quan
27 tháng 5 2022
1: \(\left(x^2+1\right)^2-4x\left(1-x^2\right)\)
\(=x^4+2x^2+1-4x+4x^3\)
\(=x^4+4x^3+2x^2-4x+1\)
\(=\left(x^2+2x-1\right)^2\)
2: \(\left(x^2-8\right)^2+36\)
\(=x^4-16x^2+64+36\)
\(=x^4-16x^2+100\)
\(=x^4+20x^2+100-36x^2\)
\(=\left(x^2+10\right)^2-\left(6x\right)^2\)
\(=\left(x^2+6x+10\right)\left(x^2-6x+10\right)\)
3: \(x^4+4=x^4+4x^2+4-4x^2\)
\(=\left(x^2+2\right)^2-4x^2\)
\(=\left(x^2+2x+2\right)\left(x^2-2x+2\right)\)
4: \(x^4+64=x^4+16x^2+64-16x^2\)
\(=\left(x^2+8\right)^2-16x^2\)
\(=\left(x^2-4x+8\right)\left(x^2+4x+8\right)\)
5: \(64x^4+1=64x^4+16x^2+1-16x^2\)
\(=\left(8x^2+1\right)^2-16x^2\)
\(=\left(8x^2-4x+1\right)\left(8x^2+4x+1\right)\)
29 tháng 6 2019
a) \(x^2+12x+35\)
\(=x^2+5x+7x+35\)
\(=\left(x^2+5x\right)+\left(7x+35\right)\)
\(=x\left(x+5\right)+7\left(x+5\right)\)
\(=\left(x+5\right)\left(x+7\right)\)
b)\(x^2-x-56\)
\(=x^2+7x-8x-56\)
\(=\left(x^2+7x\right)-\left(8x+56\right)\)
\(=x\left(x+7\right)-8\left(x+7\right)\)
\(=\left(x+7\right)\left(x-8\right)\)
c)\(5x^2-x-4\)
\(=5x^2-5x+4x-4\)
\(=\left(5x^2-5x\right)+\left(4x-4\right)\)
\(=5x\left(x-1\right)+4\left(x-1\right)\)
\(=\left(x-1\right)\left(5x+4\right)\)
29 tháng 6 2019
TL:
a)\(x^2+5x+7x+35\)
=\(x\left(x+5\right)+7\left(x+5\right)\)
=\(\left(x+7\right)\left(x+5\right)\)
b) \(x^2-x-56\)
=\(x^2+7x-8x-56\)
=\(x\left(x+7\right)-8\left(x+7\right)\)
=\(\left(x-8\right)\left(x+7\right)\)
d)\(4x^4+1=\left(2x^2\right)^2+4x^2+1-4x^2\)
=\(\left(2x^2+1\right)^2-4x^2\)
=\(\left(2x^2+1+4x\right)\left(2x^2+1-4x\right)\)
.......................(tự lm)
hc tốt
24 tháng 7 2017
a) x2-7x+6= (x-6)(x-1)
câu c,e , g tương tự nha bạn
b) x4+64= x4+16x2+64-16x2=(x2+8)2-16x2=(x2+8-4x)(x2+8+4x)
các câu còn lại cũng tượng tự nha bạn
TN
25 tháng 7 2017
\(a,x^2-7x+6=x^2-6x-x+6\)
\(=x\left(x-6\right)-\left(x-6\right)=\left(x-1\right)\left(x-6\right)\)
\(b,x^4+64=\left(x^4+16x^2+64\right)-16x^2\)
\(=\left(x^2+8\right)^2-\left(4x\right)^2=\left(x^2-4x+8\right)\left(x^2+4x+8\right)\)
\(c,x^2+12x+35=x^2+5x+7x+35\)
\(=x\left(x+5\right)+7\left(x+5\right)=\left(x+7\right)\left(x+5\right)\)
\(d,4x^4+1=\left(4x^4+4x^2+1\right)-4x^2\)
\(=\left(2x^2+1\right)-\left(2x\right)^2=\left(2x^2+2x+1\right)\left(2x^2-2x+1\right)\)
\(e,x^2-x-56=x^2-8x+7x-56\)
\(=x\left(x-8\right)+7\left(x-8\right)=\left(x+7\right)\left(x-8\right)\)
\(f,4x^2+81=\left(4x^4+36x^2+81\right)-36x^2\)
\(=\left(2x^2+9\right)^2-\left(6x\right)^2=\left(2x^2+6x+9\right)\left(2x^2-6x+9\right)\)
\(g,5x^2-x-4=5x^2-5x+4x-4\)
\(=5x\left(x-1\right)+4\left(x-1\right)=\left(5x+4\right)\left(x-1\right)\)
\(h,64x^4+y^4=\left(64x^4+16x^2y^2+y^4\right)-16x^2y^2\)
\(=\left(8x^2+y^2\right)^2-\left(4xy\right)^2=\left(8x^2+y^2+4xy\right)\left(8x^2+y^2-4xy\right)\)
25 tháng 7 2017
a) \(x^2-7x+6=x^2-6x-x+6\)
\(=x\left(x-6\right)-\left(x-6\right)\)
\(=\left(x-6\right)\left(x-1\right)\)
b) \(x^4+64=x^4+64+16x^2-16x^2\)
\(=\left(x^2+8\right)^2-\left(4x\right)^2\)
\(=\left(x^2+8-4x\right)\left(x^2+8+4x\right)\)
c) \(x^2+12x+35=x^2+5x+7x+35\)
\(=x\left(x+5\right)+7\left(x+5\right)\)
\(=\left(x+5\right)\left(x+7\right)\)
d) \(4x^4+1=4x^4+1+4x^2-4x^2\)
\(=\left(2x^2+1\right)^2-\left(2x\right)^2\)
\(=\left(2x^2+1-2x\right)\left(2x^2+1+2x\right)\)
e) \(x^2-x-56=x^2+7x-8x-56\)
\(=x\left(x+7\right)-8\left(x+7\right)\)
\(=\left(x+7\right)\left(x-8\right)\)
f) \(4x^4+81=4x^4+81+36x^2-36x^2\)
\(=\left(2x^2+9\right)^2-\left(6x\right)^2\)
\(=\left(2x^2+9-6x\right)\left(2x^2+9+6x\right)\)
g) \(5x^2-x-4=5x^2+4x-5x-4\)
\(=x\left(5x+4\right)-\left(5x+4\right)\)
\(=\left(5x+4\right)\left(x-1\right)\)
h) \(64x^4+y^4=64x^4+y^4+16x^2y^2-16x^2y^2\)
\(=\left(8x^2+y^2\right)^2-\left(4xy\right)^2\)
\(=\left(8x^2+y^2-4xy\right)\left(8x^2+y^2+4xy\right)\)
AN
27 tháng 9 2017
a) x² - x - 56
b) x^4 + 64
c) 4x^4 + 81
d) x².+ 12x + 35
e) 5x² - x - 4
g) 4x^4 + 1
h) 64x^4 + y^4
a)\(x^2-x-56\)
\(=x^2-8x+7x-56\)
\(=\left(x^2-8x\right)+\left(7x-56\right)\)
\(=x\left(x-8\right)+7\left(x-8\right)\)
\(=\left(x-8\right)\left(x+7\right)\)
b)\(x^4+64\)
\(=\left(x^2\right)^2+8^2\)
\(=\left(x^2\right)^2+16x^2+8^2-16x^2\)
\(=\left(x^2+8\right)^2-\left(4x\right)^2\)
\(=\left(x^2+8-4x\right)\left(x^2+8+4x\right)\)
c)\(4x^4+81\)
\(=\left(2x^2\right)^2+9^2\)
\(=\left(2x^2\right)^2+36x^2+9^2-36x^2\)
\(=\left(2x^2+9\right)^2-\left(6x\right)^2\)
\(=\left(2x^2+9-6x\right)\left(2x^2+9+6x\right)\)
d)\(x^2+12x+35\)
\(=x^2+5x+7x+35\)
\(=\left(x^2+5x\right)+\left(7x+35\right)\)
\(=x\left(x+5\right)+7\left(x+5\right)\)
\(=\left(x+5\right)\left(x+7\right)\)
e)\(5x^2-x-4\)
\(=5x^2-5x+4x-4\)
\(=\left(5x^2-5x\right)+\left(4x-4\right)\)
\(=5x\left(x-1\right)+4\left(x-1\right)\)
\(=\left(x-1\right)\left(5x+4\right)\)
g)\(4x^4+1\)
\(=\left(2x^2\right)^2+1^2\)
\(=\left(2x^2\right)^2+4x^2+1^2-4x^2\)
\(=\left(2x^2+1\right)^2-4x^2\)
\(=\left(2x^2+1-4x\right)\left(2x^2+1+4x\right)\)
h)\(64x^4+y^4\)
\(=\left(8x^2\right)^2+\left(y^2\right)^2\)
\(=\left(8x^2\right)^2+16x^2y^2+\left(y^2\right)^2-16x^2y^2\)
\(=\left(8x^2+y^2\right)^2-\left(4xy\right)^2\)
\(=\left(8x^2+y^2-4xy\right)\left(8x^2+y^2+4xy\right)\)
24 tháng 10 2016
Mink nghĩ đề này là phân tích đa thức thành nhân tử chứ k phải tìm x^^
a) \(x^2-x-56=x^2-8x+7x-56=x\left(x-8\right)+7\left(x-8\right)=\left(x+7\right)\left(x-8\right)\)
b) \(4x^4+1=\left(4x^4+4x^2+1\right)-4x^2=\left(2x^2+1\right)^2-\left(2x\right)^2\)
\(\left(2x^2+1-2x\right)\left(2x^2+1+2x\right)\)
c) \(5x^2-x-4=5x^2-5x+4x-4=5x\left(x-1\right)+4\left(x-1\right)=\left(x-1\right)\left(5x+4\right)\)
d) \(4x^4+81=\left(4x^4+36x^2+81\right)-36x^2=\left(2x^2+9\right)^2-\left(6x\right)^2\)
\(=\left(2x^2+9+6x\right)\left(2x^2+9-6x\right)\)
e) \(64x^4+y^4=\left(64x^4+16x^2y^2+y^4\right)-\left(4xy\right)^2=\left(8x^2+y^2\right)^2-\left(4xy\right)^2\)
\(=\left(8x^2+y^2-4xy\right)\left(8x^2+y^2+4xy\right)\)
24 tháng 10 2016
a)\(x^2-x-56\)
\(=x^2+7x-8x-56\)
\(=x\left(x+7\right)-8\left(x+7\right)\)
\(=\left(x-8\right)\left(x+7\right)\)
b)\(4x^4+1\)
\(=\left(2x+1\right)^2-4x^2\)
\(=\left(2x^2-2x+1\right)\left(2x^2+2x+1\right)\)
c)\(5x^2-x-4\)
\(=5x^2+4x-5x-4\)
\(=x\left(5x+4\right)-\left(5x+4\right)\)
\(=\left(x-1\right)\left(5x+4\right)\)
d)\(4x^4+81\)
\(=\left(2x^2\right)^2+9^2+36x^2-36x^2\)
\(=\left(2x^2+9\right)^2-36x^2\)
\(=\left(2x^2-6x+9\right)\left(2x^2+6x+9\right)\)
e)\(64x^4+y^4\)
\(=\left(8x^2\right)^2+y^4+16x^2y^2-16x^2y^2\)
\(=\left(8x^2+y^2\right)^2-\left(4xy\right)^2\)
\(=\left(8x^2+y^2-4xy\right)\left(8x^2+y^2+4xy\right)\)
a) = \(4x^4+4x^2+1\)
= \(\left(2x^2+1\right)^2\)
b) = \(4x^4+36x^2+81-36x^2\)
= \(\left(2x^2+9\right)^2\)
c) = \(64x^4+16x^2y^2+y^4-16x^2y^2\)
= \(\left(8x^2+y^2\right)^2\)
d) = \(x^8+4x^4+4-4x^4\)
= \(\left(x^4+2\right)^2\)
e) = \(\left(x^4+2x^2+1\right)-x^2\)
= \(\left(x^2+1\right)^2-x^2\)
= \(\left(x^2+1-x\right).\left(x^2+1+x\right)\)
f) = \(\left(x^7-x\right)+\left(x^5-x^2\right)+\left(x^2+x+1\right)\)
= \(x.\left(x^3-1\right).\left(x^3+1\right)+x^2.\left(x^3-1\right)+\left(x^2+x+1\right)\)
\(\left(x^2+x+1\right).\left(x-1\right).\left(x^4+x\right)+x^2.\left(x-1\right).\left(x^2+x+1\right)+\left(x^2+x+1\right)=\left(x^2+x+1\right).\left(x^5-x^4+x^3-1+1\right)\)
c/=64x^4+16x^2y^2+y^4-16x^2y^2
=(8x^2+y^2)^2-(4xy)^2
=(8x^2+y^2+4xy)(8x^2+y^2-4xy)