\(27y^3-9y^2+y-\frac{1}{27}\)

\(=\left(3y\right)^3-3.\left(3y\right)^2.\frac{1}{3}+3.3y.\left(\frac{1}{3}\right)^2-\left(\frac{1}{3}\right)^3\)

\(=\left(3y-\frac{1}{3}\right)^3\)

hk

tốt

7 Năm Rồi Ư!?

2xy + x² + y² = ( x + y )² = ( x+y ) ( x + y )

( 25z -15n )² = ( 25z - 15n ) ( 25z -15n )

\(\left(A+B\right)^2=A^2+2AB+B^2\)

\(\left(A-B\right)^2=A^2-2AB+B^2\)

\(2xy+x^2+y^2=x^2+2.x.y+y^2=\left(x+y\right)^2\)\(\left(25z-15n\right)^2=\left(25n\right)^2-2.25z.15n+\left(15n\right)^2=625z^2-375zn+225n^2\)

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

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

=(a-2b-2b)(a-2b+2b)

=a(a-4b)

b: \(\left(a-b\right)^2-c^2=\left(a-b-c\right)\left(a-b+c\right)\)

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

d: \(\left(a+3b\right)^2-9b^2\)

\(=\left(a+3b\right)^2-\left(3b\right)^2\)

=(a+3b-3b)(a+3b+3b)=a(a+6b)

e: \(\left(x-3\right)^3-27\)

\(=\left(x-3-3\right)\left\lbrack\left(x-3\right)^2+3\left(x-3\right)+9\right\rbrack\)

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

f: \(\left(x+1\right)^3-125\)

\(=\left(x+1-5\right)\left\lbrack\left(x+1\right)^2+5\left(x+1\right)+25\right\rbrack\)

\(=\left(x-4\right)\left(x^2+2x+1+5x+5+25\right)=\left(x-4\right)\left(x^2+7x+31\right)\)

dấu ^ là mũ nha mn

\(x^2-2=\left(x-\sqrt{2}\right)\left(x+\sqrt{2}\right)\)

\(27x^3-a^3b^3\)

\(=\left(3x\right)^3-\left(ab\right)^3\)

\(=\left(3x-ab\right)\left[\left(3x\right)^2+3x\cdot ab+\left(ab\right)^2\right]\)

\(=\left(3x-ab\right)\left(9x^2+3xab+a^2b^2\right)\)

27x³ - a³b³

= (3x)³ - (ab)³

= (3x - ab)(9x² + 3xab + a²b²)

Mở sách ra, SGK ghi to thế còn j;-;

\(\left(a-b\right)^3=a^3-3a^2b+3ab^2-b^3\)

x³+64=x³+4³=(x+4)(x²-4x+4²)=(x+4)(x²-4x+16)

\(x^3+64=x^3+4^3=(x+4)(x^2-3x+16)\)

\(10x-25-x^2=-\left(x^2-10x+25\right)\)

\(=-\left(x^2-2.x.5+5^2\right)=-\left(x-5\right)^2\)

10x - 25 - x²

= x²- 10x - 25

= - ( x² +10x +25)

= -(x² + 2.x.5+5² )

= - (x+5 )²