Phân tích thành nhân tử đúng không ạ

a, (m+n)(m-n)

b, 4(m-2n)(m+2n)

a_ $m^2-n^2 = (m-n)(m+n)$

b_ $4m^2-16n^2$

$ = (2m)^2 - (4n)^2$

$  = (2m-4n)(2m+4n)$

$ = 4.(m-2n)(m+2n)$

a.

$x^2+20x+100=(x+10)^2$

b.

$16x^2+24xy+9y^2=(4x+3y)^2$

c.

$y^2-14y+49=(y-7)^2$
d.

$9x^2-42xy+49y^2=(3x-7y)^2$

e.

$4x^2-9y^2=(2x-3y)(2x+3y)$

f.

$16-x^2=(4-x)(4+x)$

g.

$49x^2-1=(7x-1)(7x+1)$

h.

$16x^2-25=(4x-5)(4x+5)$

i.

$8x^3+24x^2y+54xy^2+27y^3=(2x+3y)^3$

k.

$x^3-6x^2y+12xy^2-8y^3=(x-2y)^3$

l.

$(2a+b)(4a^2-2ab+b^2)=(2a)^3+b^3=8a^3+b^3$

m.

$(3x-4y)(9x^2+12xy+16y^2)=(3x)^3-(4y)^3=27x^3-64y^3$

\(a,=\left(x+\dfrac{5}{2}\right)^2\\ b,=\left(2x+3y\right)^2\\ c,=a^2+b^2+c^2+2ab-2bc-2ac\\ d,=\left(4x-1\right)^2\\ e,=a^2+b^2+c^2+2ab+2bc+2ac\\ f,=a^2+b^2+c^2-2ab+2bc-2ac\)

a: \(\left(3x-1\right)\left(9x^2+3x+1\right)=27x^3-1\)

b: \(\left(1-\dfrac{x}{5}\right)\left(\dfrac{x^2}{25}+\dfrac{x}{5}+1\right)=1-\dfrac{x^3}{125}\)

c: \(\left(x+3y\right)\left(x^2-3xy+9y^2\right)=x^3+27y^3\)

d: \(\left(4x+3y\right)\left(16x^2-12xy+9y^2\right)=64x^3+27y^3\)

\(a,=\left(x+1\right)^2\\ b,=\left(y-2\right)^2\\ c,=\left(x-3\right)^2\\ d,=\left(a-7\right)^2\\ e,=\left(m-2\right)^2\\ f,=\left(2x-1\right)^2\\ g,=\left(a+5\right)^2\\ h,=\left(z-10^2\right)\\ i,=\left(x+3y\right)^2\\ j,=\left(2x-5b\right)^2\\ k,=\left(a+5\right)^2\\ l,=\left(x^2+1\right)^2\\ m,=\left(y^3-1\right)^2=\left(y-1\right)^2\left(y^2+y+1\right)^2\\ n,=\left(c^5-5\right)^2\\ o,=\left(3x^2+2y\right)^2\\ p,=5m^2n^3\left(5m^2n^3-2\right)\)

\(a.6x^3y^2.\left(2-x\right)+9x^2y^2.\left(x-2\right)\\ =6x^3y^2.\left(2-x\right)-9x^2y^2.\left(2-x\right)\\ =3x^2y^2\left(2-x\right)\left(2x-3\right)\)

Lời giải:

a.

$=6x^3y^2(2-x)-9x^2y^2(2-x)$

$=(2-x)(6x^3y^2-9x^2y^2)$

$=(2-x).3x^2y^2(2x-3)=3x^2y^2(2-x)(2x-3)$

b.

$=(x^2-y^2)-(4x-4y)=(x-y)(x+y)-4(x-y)$

$=(x-y)(x+y-4)$

c.

$81x^2-(9y^2-6yz+z^2)$

$=(9x)^2-(3y-z)^2=(9x-3y+z)(9x+3y-z)$

\(3x^2\left(a-b+c\right)+36xy\left(a-b+c\right)+108y^2\left(a-b+c\right)\)

\(=\left(a-b+c\right)\left(3x^2+36xy+108y^2\right)\)

\(=3\left(a-b+c\right)\left(x^2+12xy+36y^2\right)\)

\(=3\left(a-b+c\right)\left(x+6y\right)^2\)

___________________

\(x^2-2xy+y^2-4m^2+4mn-n^2\)

\(=\left(x^2-2xy+y^2\right)-\left(4m^2-4mn+n^2\right)\)

\(=\left(x-y\right)^2-\left(2m-n\right)^2\)

\(=\left(x-y-2m+n\right)\left(x-y+2m-n\right)\)

b: \(8x^2-48x+6xy-36y\)

\(=8x\left(x-6\right)+6y\left(x-6\right)\)

\(=2\left(x-6\right)\left(4x+3y\right)\)

d: \(a^2-2ab+b^2-4\)

\(=\left(a-b\right)^2-4\)

\(=\left(a-b-2\right)\left(a-b+2\right)\)