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a, = (x+3y)^2
b, = (x-1/2)(x+1/2)
c, = (x-5)^2
d, = (2x+3y)(4x^2-6xy+9y^2)
e, = (x^3-y)^2
f,= (x+3y)^3
\(a,x\left(x^2+4x+4\right)=x\left(x+2\right)^2\)
\(b,x\left(y+1\right)+y+1=\left(x+1\right)\left(y+1\right)\)
\(c,\left(x+y\right)^2-9z^2=\left(x+y-3z\right)\left(x+y+3z\right)\)
\(d,5\left(x^2-2x+1-y^2\right)=5\left(\left(x+1\right)^2-y^2\right)=5\left(x+1-y\right)\left(x+1+y\right)\)
Câu 2 nha
\(a,x^4+2x^3+x^2\)
\(=x^2\left(x^2+2x+1\right)\)
\(=x^2\left(x+1\right)^2\)
\(c,x^2-x+3x^2y+3xy^2+y^3-y\)
\(=\left(x^3+3x^2y+3xy^2+y^3\right)-\left(x+y\right)\)
\(=\left(x+y\right)^3-\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2+2xy+y^2-1\right)\)
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 . 5(x-y)-y(x-y)
=(x6-y)(5-y)
B . x^2 - xy - 8x+8y
=(x^2-xy)-(8x-8y))
=x(x-y) - 8(x-y)
C. x^2-10x+25 - y^2
=(x^2 - 10x + 25 ) - y^2
=(x-5)^2 - y^2
=(x-5+y)(x-5-y)
D . x^3 - 3x^2-4x+12
=(x^3 - 3x^2 ) - (4x - 12)
=x^2 (x-3)-4(x-3)
=(x^2-4)(x-3)
=(x+2)(x-2)(x-3)
D . 2x^2-2y^2- 6x-6y
=(2^x - 2y^2) - (6x+ 6y)
=2(x^2 - y^2) - 6(x+y)
=2(x+y)(x-y) - 6(x+y)
=2(x+y)(x-y-3)
E . x^3 - 3x^2 + 3x - 1
=(x-1)^3
D.x^2+3x+2
=x^2+2x+x+2
=(x^2+2x)+(x+2)
=x(x+2)+(x+2)
=(x+2)(x+1)
a) \(x^2+8x+15=x^2+3x+5x+15=\left(x+3\right)\left(x+5\right)\)
b) \(x^2+3x+2=x^2+2x+x+2=\left(x+1\right)\left(x+2\right)\)
c) \(-x^2+7x-6=-x^2+x+6x-6=\left(-x+6\right)\left(x-1\right)\)
d) \(5x^3y-10x^2y^2+5xy^3=5xy\left(x^2-2xy+y^2\right)=5xy\left(x-y\right)^2\)
e) \(2x^2+7x-15=2x^2-3x+10x-15=\left(2x-3\right)\left(x+5\right)\)
\(\frac{2}{5}x\left(y-1\right)-\frac{2}{5}y\left(y-1\right)\)
\(=\left(y-1\right)\left[\left(\frac{2}{5}x-\frac{2}{5}y\right)\right]\)
\(=\left(y-1\right)\frac{2}{5}\left(x-y\right)\)
a) \(x^2+6x+9\)
\(=\left(x+3\right)^2\)
\(=\left(x+3\right)\left(x+3\right)\)
b) \(10x-25-x^2\)
\(=-\left(x^2-10x+25\right)\)
\(=-\left(x-5\right)^2\)
\(=-\left(x-5\right)\left(x-5\right)\)
c) \(8x^3-\frac{1}{8}\)
\(=\left(2x\right)^3-\left(\frac{1}{2}\right)^3\)
\(=\left(2x-\frac{1}{2}\right)\left(4x^2+x+\frac{1}{4}\right)\)
d) \(\frac{1}{25}x^2-64y^2\)
\(=\left(\frac{1}{5}x\right)^2-\left(8y\right)^2\)
\(=\left(\frac{1}{5}x-8y\right)\left(\frac{1}{5}x+8y\right)\)
a) \(x^2+6x+9=x^2+2.3.x+3^2\)\(=\left(x+3\right)^2\)
b)\(10x-25-x^2=-\left(x^2-10x+25\right)\)\(=-\left(x^2-2.5.x+5^2\right)=-\left(x+5\right)^2\)
c)\(8x^3-\frac{1}{8}=\left(2x\right)^3-\left(\frac{1}{2}\right)^3\)\(=\left(2x-\frac{1}{2}\right)\left(4x+x+\frac{1}{4}\right)\)
d)\(\frac{1}{25}x^2-64y^2=\left(\frac{1}{5}\right)^2-\left(8y\right)^2\)\(=\left(\frac{1}{5}-8y\right)\left(\frac{1}{5}+8y\right)\)
\(a,=5xy\left(3x-y+4x^2\right)\)
\(b,=\left(x-4\right)^2-16=\left(x-4+4\right)\left(x-4-4\right)\)
\(=x\left(x-8\right)\)
\(c,=\left(x-5\right)^2-9^2=\left(x-14\right)\left(x+4\right)\)
\(d,=\left(x-y\right)^2-\left(x+5\right)^2=\left(2x-y+5\right)\left(-y-5\right)\)
a) \(15x^2y-5xy^2+20x^3y=5xy\left(3x-y+4x^2\right)\)
b) \(x^2+16-8x-16=x^2-8x=x\left(x-8\right)\)
c) \(x^2+25-10x-81=\left(x-5\right)^2-9^2=\left(x-14\right)\left(x+4\right)\)
d) \(x^2-2xy+y^2-x^2-10x-25=\left(x-y\right)^2-\left(x+5\right)^2=-\left(2x-y+5\right)\left(y+5\right)\)