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1) \(4x^2+4x+1=\left(2x+1\right)^2\)
2)\(9x^2-24xy+16y^2=\left(3x-4y\right)^2\)
3)\(-x^2+10x-25=-\left(x-5\right)^2\)
4)\(1+12x+36x^2=\left(1+6x\right)^2\)
5) \(\dfrac{x^2}{4}+2xy+4y^2=\left(\dfrac{x}{2}+2y\right)^2\)
6) \(4x^2+4xy+y^2=\left(2x+y\right)^2\)
a, \(x^2+10x+25=x^2+5x+5x+25\)
\(=\left(x+5\right)^2\)
b, \(x^2-12x+36=x^2-6x-6x+36\)
\(=\left(x-6\right)^2\)
c, \(9x^2+4+12x=9x^2+6x+6x+4\)
\(=3x\left(3x+2\right)+2\left(3x+2\right)=\left(3x+2\right)^2\)
d, \(x^2+49-14x=x^2-7x-7x+49\)
\(=\left(x-7\right)^2\)
e, \(9x^4+24x^2+16=9x^4+12x^2+12x^2+16\)
\(=3x^2\left(3x^2+4\right)+4\left(3x^2+4\right)=\left(3x^2+4\right)^2\)
g,\(4x^2-12xy+9y^2=4x^2-6xy-6xy+9y^2\)
\(=2x\left(2x-3y\right)-3y\left(2x-3y\right)=\left(2x-3y\right)^2\)
Chúc bạn học tốt!!!
Bài làm:
a) \(x^6-6x^4+12x^2-8\)
\(=\left(x^2-2\right)^3\)
b) \(x^2+16-8x=\left(x-4\right)^2\)
c) \(10x-x^2-25=-\left(x-5\right)^2\)
d) \(9\left(a-b\right)^2-4\left(x-y\right)^2\)
\(=\left[3\left(a-b\right)\right]^2-\left[2\left(x-y\right)\right]^2\)
\(=\left(3a-3b-2x+2y\right)\left(3a-3b+2x-2y\right)\)
e) \(\left(x+y\right)^2-2xy+1\)
\(=x^2+2xy+y^2-2xy+1\)
\(=x^2+y^2+1\)
sai sai
a. \(x^6-6x^4+12x^2-8=\left(x^2\right)^3-3\left(x^2\right)^2.2+3x^22-2^3=\left(x^2-2\right)^3\)
b. \(x^2+16-8x=x^2-8x+4^2=\left(x-4\right)^2\)
c. \(10x-x^2-25=10x-x^2-5^2=-\left(x-5\right)^2\)
d. \(9\left(a-b\right)^2-4\left(x-y\right)^2=\left[3\left(x-y\right)-2\left(x+y\right)\right]\left[3\left(x-y\right)+2\left(x+y\right)\right]\)
\(=\left(3x-3y-2x-2y\right)\left(3x-3y+2x+2y\right)=\left(x-5y\right)\left(5x-y\right)\)
e. \(\left(x+y\right)^2-2xy+1=x^2+2xy+y^2-2xy+1=x\left(x+2y\right)-y\left(y+2x\right)+2y^2+1\)
\(=x\left(x+y\right)-y\left(y+x\right)+xy-yx+2y^2+x=\left(x-y\right)\left(x+y\right)+2y^2+x\)
a , \(16x^2+8x+1=\left(4x\right)^2+2.4x.1+1^2=\left(4x+1\right)^2\)
b , \(x^2-x+\dfrac{1}{4}=x^2-2.x.\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2=\left(x-\dfrac{1}{2}\right)^2\)
a,(4x+1)2 e,\(\left(\dfrac{3}{2}x-\dfrac{2}{5}\right)^2\)
b,(x-\(\dfrac{1}{2}\))2 g,\(\left(xy+1\right)^2\)
c,(\(x+\dfrac{3}{2}\))2 h,\(\left(x+5\right)^2\)
d,\(\left(x-\dfrac{5}{4}\right)^2\) i,\(-\left(x-6\right)^2\)
k,\(-\left(2x+3\right)^2\)
Bài 1:
a) \(\dfrac{15xy}{10x^2y}\)
= \(\dfrac{3.5xy}{2.5xyx}\)
= \(\dfrac{3}{2x}\)
d) \(\dfrac{6x\left(x+5\right)^3}{2x^2\left(x+5\right)}\)
= \(\dfrac{3.2x\left(x+5\right)\left(x+5\right)^2}{x.2x\left(x+5\right)}\)
= \(\dfrac{3\left(x+5\right)^2}{x}\)
a, (x+2)^2
b, (x-3)^2
c, (2x+3)^2
d, (3x-1)^2
e, (x+5)^2
g, (4x-1)^2
a) x2 + 4x + 4 = ( x + 2 )2
b) x2 - 6x + 9 = (x-3)2
c) 4x2 + 12x + 9 = (2x)2 + 2.2x.3 + 3^2 = (2x + 3)2
d) 9x2 - 6x + 1 = (3x)2 - 2.3x.1 + 1^2 = (3x-1)2
e) x2 + 25 +10x = x2 + 2.x.5 + 52 = (x+5)2
g) 16x2 +1 - 8x = (4x)2 - 2.4x.1 + 1^2 = (4x-1)2
Dài dữ trời :V Về sau gửi từng bài một thôi, nhìn hoa mắt quá @@
B1: Phân tích thành nhân tử:
a) \(6x^2+9x=3x\left(2x+3\right)\)
b) \(4x^2+8x=4x\left(x+2\right)\)
c) \(5x^2+10x=5x\left(x+2\right)\)
d) \(2x^2-8x=2x\left(x-4\right)\)
e) \(5x-15y=5\left(x-3y\right)\)
f) \(x\left(x^2-1\right)+3\left(x^2-1\right)=\left(x^2-1\right)\left(x+3\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x+3\right)\)
g) \(x^2-2x+1-4y^2=\left(x-1\right)^2-4y^2\)
\(=\left(x-1-2y\right)\left(x-1+2y\right)\)
h) \(x^2-100=\left(x-10\right)\left(x+10\right)\)
i) \(9x^2-18x+9=\left(3x-3\right)^2\)
k) \(x^3-8=\left(x-2\right)\left(x^2+2x+4\right)\)
l) \(x^2+6xy^2+9y^4=\left(x+3y\right)^2\)
m) \(4xy-4x^2-y^2=-\left(4x^2-4xy+y^2\right)\)
\(=-\left(2x-y\right)^2\)
n) \(\left(x-15\right)^2-16=\left(x-15-16\right)\left(x-15+16\right)\)
\(=\left(x-31\right)\left(x+1\right)\)
o) \(25-\left(3-x\right)^2=\left(5-3+x\right)\left(5+3+x\right)\)
\(=\left(2+x\right)\left(8+x\right)\)
p) \(\left(7x-4\right)^2-\left(2x+1\right)^2\)
\(=\left(7x-4-2x-1\right)\left(7x-4+2x+1\right)\)
\(=\left(5x-5\right)\left(9x-3\right)\)
Bài 1 :
a ) \(6x^2+9x=3x\left(x+3\right)\)
b ) \(4x^2+8x=4x\left(x+2\right)\)
c ) \(5x^2+10x=5x\left(x+2\right)\)
d ) \(2x^2-8x=2x\left(x-4\right)\)
e ) \(5x-15y=5\left(x-3y\right)\)
f ) \(x\left(x^2-1\right)+3\left(x^2-1\right)=\left(x^2-1\right)\left(x+3\right)\)
g ) \(x^2-2x+1-4y^2=\left(x-1\right)^2-\left(2y\right)^2=\left(x-1-2y\right)\left(x-1+2y\right)\)
h ) \(x^2-100=x^2-10^2=\left(x-10\right)\left(x+10\right)\)
i ) \(9x^2-18x+9=\left(3x-3\right)^2\)
k ) \(x^3-8=\left(x-2\right)\left(x^2+2x+2^2\right)\)
l ) \(x^2+6xy^2+9y^4=\left(x+3y^2\right)^2\)
m ) \(4xy-4x^2-y^2=-\left(2x-y\right)^2\)
n ) \(\left(x-15\right)^2=x^2-30x+15^2\)
o ) \(25-\left(3-x\right)^2=\left(5-3+x\right)\left(5+3-x\right)=\left(2+x\right)\left(8-x\right)\)
p ) \(\left(7x-4\right)^2-\left(2x+1\right)^2=\left(7x-4-2x-1\right)\left(7x-4+2x+1\right)=\left(5x-5\right)\left(9x-3\right)\)
Bài 2 :
a ) \(3x^3-6x^2+3x^2y-6xy=3x\left(x^2-2x+xy-2y\right)\)
b ) \(x^2-2x+xy-2y=x\left(x-2\right)+y\left(x-2\right)=\left(x-2\right)\left(x+y\right)\)
c ) \(2x+x^2-2y-2xy=......................\)
d ) \(x^2-2xy+y^2-9=\left(x-y\right)^2-3^2=\left(x-y-3\right)\left(x-y+3\right)\)
e ) \(x^2+y^2-2xy-4=\left(x-y\right)^2-2^2=\left(x-y-2\right)\left(x-y+2\right)\)
f )\(2xy-x^2-y^2+9=-\left(x-y\right)^2+9=3^2-\left(x-y\right)^2=\left(3-x+y\right)\left(3+x-y\right)\)
Câu trên mình trả lời rồi nha
đề là gì bạn có phải như mình làm ko
\(x^2+6x+9=\left(x+3\right)^2\)
\(x^2+8x+16=\left(x+4\right)^2\)
\(x^2+10x+25=\left(x+5\right)^2\)
\(x^2-12+36=\left(x-6\right)^2\)
\(x^2-14x+49=\left(x-7\right)^2\)