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\(4x^4+81=\left(2x\right)^2+2.2x^2.9+9^2-36x^2\)
\(=\left(2x^2+9\right)^2-\left(6x\right)^2=\left(2x^2-6x+9\right)\left(2x^2+6x+9\right)\)
\(64x^4+y^4=\left(8x^2\right)^2+2.8x^2.y^2+\left(y^2\right)^2-16x^2y^2\)
\(=\left(8x^2+y^2\right)^2-\left(4xy\right)^2=\left(8x^2-4xy+y^2\right)\left(8x^2+4xy+y^2\right)\)
\(x^2-y^2+4x+4\)
\(=\left(x+2\right)^2-y^2\)
\(=\left(x+2+y\right)\left(x+2-y\right)\)
\(4x^2-y^2+8\left(y-2\right)\)
\(=4x^2-\left(y^2-8y+16\right)\)
\(=4x^2-\left(y-4\right)^2\)
\(=\left(2x+y-4\right)\left(2x-y+4\right)\)
dat \(x^2-2x+2=y\)
ta co pt
\(y^4+20x^2y^2+64x^4\)
\(=\left(8x^2\right)^2+2.8x^2.\frac{10}{8}y^2+\left(\frac{10^{ }}{8^{ }}y^2\right)^2-\frac{36}{64}y^4\)
\(=\left(8x^2+\frac{10}{8}y^2\right)^2-\left(\frac{6}{8}y^2\right)^2\)
\(=\left(8x^2+\frac{y^2}{2}\right)\left(8x^2+2y^2\right)\)
bạn thay y nữa là xong
\(\left(x^2-2x+2\right)^4+20x^2\left(x^2-2x+2\right)^2+64x^4\)
\(=\left(x^2-2x+2\right)^4+20x^2\left(x^2-2x+2\right)^2+100x^4-36x^4\)
\(=\left[\left(x^2-2x+2\right)^2+10x^2\right]^2-36x^4\)
\(=\left(x^4-4x^3+18x^2-8x+4\right)^2-\left(6x^2\right)^2\)
\(=\left(x^4-4x^3+24x^2-8x+4\right)\left(x^4-4x^3+12x^2-8x+4\right)\)
\(\left(x^2-2x+2\right)^4+20x^2\left(x^2-2x+2\right)+64x^4\)
=\(\left[\left(x^2-2x+2\right)^4+2.10x^2\left(x^2-2x+2\right)^2+100x^4\right]\)-100x4+64x2
=\(\left[\left(x^2-2x+2\right)^2+10x^2\right]^2-36x^2\)
=\(\left[\left(x^2-2x+2\right)^2+4x^2\right].\left[\left(x^2-2x+2\right)^2+16x^2\right]\)
a, 4x2 - 12x + 9
= (2x + 3)2
b, 9x4y3 + 3x2y4
= 3x2y3(3x2 + y)
c, ( x - 3 )2 - 2x ( x - 3 )
= (x - 3)(x - 3 - 2x)
= (x - 3)(-x - 3)
d, 3x ( x - 1 ) + 6 ( x - 1 )
= 3(x - 1)(x + 2)
e, 2x ( x + 1 ) - 4x - 4
= 2x(x + 1) - 4(x + 1)
= (x + 1)(2x - 4)
= 2(x + 1)(x - 2)
f, ( 2x - 3 )2 - 4x + 6
= (2x - 3)2 - 2(2x - 3)
= (2x - 3)(2x - 3 - 2)
= (2x - 3)(2x - 5)
a)\(3x^2-8x+4\)
\(=3x^2-2x-6x+4\)
\(=x\left(3x-2\right)-2\left(3x-2\right)\)
\(=\left(x-2\right)\left(3x-2\right)\)
b)\(4x^4+81\)
\(=4x^4+36x^2+81-36x^2\)
\(=\left(2x^2+9\right)^2-36x^2\)
\(=\left(2x^2-6x+9\right)\left(2x^2+6x+9\right)\)
c)\(x^8+98x^4+1\)
\(=\left(x^8+2x^4+1\right)+96x^4\)
\(=\left(x^4+1\right)^2+16x^2\left(x^4+1\right)+64x^4-16x^2\left(x^4+1\right)+32x^4\)
\(=\left(x^4+8x^2+1\right)^2-16x^2\left(x^4-2x^2+1\right)\)
\(=\left(x^4+8x^2+1\right)^2-16x^2\left(x^4-2x^2+1\right)\)
\(=\left(x^4+8x^2+1\right)^2-\left(4x^3-4x\right)^2\)
\(=\left(x^4+4x^3+8x^2-4x+1\right)\left(x^4-4x^3+8x^2+4x+1\right)\)
d)\(x^4+6x^3+7x^2-6x+1\)
\(=x^4+3x^3-x^2+3x^3+9x^2-3x-x^2-3x+1\)
\(=x^2\left(x^2+3x-1\right)+3x\left(x^2+3x-1\right)-\left(x^2+3x-1\right)\)
\(=\left(x^2+3x-1\right)\left(x^2+3x-1\right)\)\(=\left(x^2+3x-1\right)^2\)
x4+x=x(x3+1)=x(x+1)(x2-x+1)
x4+64=x4+16x2+64-16x2=(x2+8)2-(4x)2=(x2+8+4x)(x2+8-4x)
4x4+81=4x4+36x2+81-36x2=(2x2+9)2-(6x)2=(2x2+9+6x)(2x2+9-6x)
64x4+y4=64x4+16(xy)2+y4-16(xy)2=(8x2+y2)-(4xy)2=(8x2+y2-4xy)(8x2+y2=4xy)
x4+4y4=x4+4(xy)2+4y4-4(xy)2=(x2+2y2-2xy)(x2+2y2+2xy)
x4+x2+1=(x4+2x2+1)-x2=(x2+1-x)(x2+1+x)
Mình làm có vài đoạn hơi tắt nha.
a)x4-4(x2+5)-25=x4-4x2-45=(x4-9x2)+(5x2-45)=x2(x2-9)+5(x2-9)=(x2-9)(x2+5)=(x-3)(x+3)(x2+5)
b)a2-b2-2a+1=(a2-2a+1)-b2=(a-1)2-b2=(a-b-1)(a+b-1)
c)x2-2x-4y2-4y=(x2-2x+1)-(4y2+4y+1)=(x-1)2-(2y+1)2=(x-1-2y-1)(x-1+2y+1)=(x-2y-2)(x+2y)
d)x2+4x-y2+4=(x2+4x+4)-y2=(x+2)2-y2=(x-y+2)(x+y+2)
\(\left(2x+1\right)^2-4\left(x-1\right)^2=3\left(4x-1\right)\)
\(\left(2x+y\right)^2-4x^2+12x-9=\left(2x+y\right)^2-\left(2x-3\right)^2=\left(y+3\right)\left(4x+y-3\right)\)
\(\left(x+1\right)^2-4\left(x+1\right)\left(y^2+4y^4\right)=\left(x+1\right)\left(x-16y^4-4y^2+1\right)\)
\(a,\left(2x+1\right)^2-4\left(x-1\right)^2=\left(2x+1-2\left(x-1\right)\right)\left(2x+1+2\left(x-1\right)\right)\)
\(=\left(2x+1-2x+2\right)\left(2x+1+2x-2\right)\)
\(=3\left(4x-1\right)\)
\(b,\left(2x+y\right)^2-4x^2+12x-9=\left(2x+y\right)^2-\left(2x-3\right)^2\)
\(=\left(2x+y-2x+3\right)\left(2x+y+2x-3\right)\)
\(=\left(y+3\right)\left(4x+y-3\right)\)
\(c,\left(x+1\right)^2-4\left(x+1\right)\left(y^2+4y^4\right)=\left(x+1\right)\left(x+1-4\left(y^2+4y^4\right)\right)\)
\(=\left(x+1\right)\left(x+1-4y^2+16y^4\right)\)
a) Ta có: \(4x^4+81\)
\(=\left(2x^2\right)^2+9^2+2\cdot2x^2\cdot9-36x^2\)
\(=\left(2x^2+9\right)^2-\left(6x\right)^2\)
\(=\left(2x^2-6x+9\right)\left(2x^2+6x+9\right)\)
b) Ta có: \(64x^4+y^4\)
\(=\left(8x^2\right)^2+\left(y^2\right)^2+2\cdot8x^2\cdot y^2-16x^2y^2\)
\(=\left(8x^2+y^2\right)^2-\left(4xy\right)^2\)
\(=\left(8x^2-4xy+y^2\right)\left(8x^2+4xy+y^2\right)\)
c) Ta có: \(\left(2x^2-4\right)^2+9\)
\(=4x^4-16x^2+16+9\)
\(=4x^4-16x^2+25\)
\(=4x^4+20x^2+25-36x^2\)
\(=\left(2x^2+5\right)^2-\left(6x\right)^2\)
\(=\left(2x^2-6x+5\right)\left(2x^2+6x+5\right)\)
Lời giải:
a) $4x^4+81=(2x^2)^2+9^2=(2x^2)^2+9^2+2.2x^2.9-36x^2$
$=(2x^2+9)^2-(6x)^2=(2x^2+9-6x)(2x^2+9+6x)$
b)
$64x^4+y^4=(8x^2)^2+(y^2)^2+2.8x^2.y^2-16x^2y^2$
$=(8x^2+y^2)^2-(4xy)^2=(8x^2+y^2-4xy)(8x^2+y^2+4xy)$
c) Biểu thức không phân tích được thành nhân tử.