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

c: \(x^3-125=\left(x-5\right)\left(x^2+5x+25\right)\)

\(\dfrac{1}{8}x^3-64=\left(\dfrac{1}{2}x-4\right)\left(\dfrac{1}{4}x^2+2x+16\right)\)

d: \(=\left(2x+5y\right)^3\)

1.\(x^{16}-y^{16}=\left(x^8-y^8\right)\left(x^8+y^8\right)\)

2.\(x^3-125=x^3-5^3=\left(x-5\right)\left(x^2+5x+25\right)\)

\(-64+\frac{1}{8}x^3=\left(\frac{x}{2}\right)^3-4^3=\left(\frac{x}{2}-4\right)\left(\frac{x^2}{4}+2x+16\right)\)

\(8x^3+60x^2y+150xy^2+125y^3=\left(2x\right)^3+3.\left(2x\right)^2.\left(5y\right)+3.\left(2x\right).\left(5y\right)^2+\left(5y\right)^3\)

\(=\left(2x+5y\right)^3\)

cám ơn bn Nguyễn Minh Quang nhé

\(8x^3+60x^2y+150xy^2+125y^3=\left(2x\right)^3+3.\left(2x\right)^2.5y+3.2x.\left(5y\right)^2+\left(5y\right)^3\)

\(=\left(2x+5y\right)^3\)

Bài 1:

a) -16 +(x-3)²

<=> (x-3)²-16

<=> (x-3)² -4²

<=> (x-3-4)(x-3+4)

<=> (x-7)(x+1)

b) 64+16y+y²

<=> y² + 2.8.y + 8²

<=> (y+8)²

c) \(\dfrac{1}{8}-8x^3\)

\(\Leftrightarrow\left(\dfrac{1}{2}\right)^3-\left(2x\right)^3\)

\(\Leftrightarrow\left(\dfrac{1}{2}-2x\right)\left(\dfrac{1}{4}+x+4x^2\right)\)

d)\(x^2-x+\dfrac{1}{4}\)

\(\Leftrightarrow x^2-2.\dfrac{1}{2}.x+\left(\dfrac{1}{2}\right)^2\)

\(\Leftrightarrow\left(x-\dfrac{1}{2}\right)^2\)

e) x⁴ + 4x² + 4

<=> (x²)² + 2.2.x² +2²

<=> (x² + 2)²

g)\(8x^3+60x^2y+150xy^2+125y^3\)

\(\Leftrightarrow\left(2x+5y\right)^3\)

(2x+5y)^3

Làm bài 1 thôi !! Mấy bài kia tương tự . Tìm nhân tử chung ra .

a) \(m^2-n^2=\left(m-n\right)\left(m+n\right)\)

b) \(\left(x^2+x-1\right)^2-\left(x^2+2x+3\right)^2=\left(x^2+x-1+x^2+2x+3\right)\left(x^2+x-1-x^2-2x-3\right)\)

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

c) \(-16+\left(x-3\right)^2=\left(x-3+4\right)\left(x-3-4\right)=x\left(x-7\right)\)

d) \(64+16y+y^2=\left(y+8\right)\left(y+8\right)\)

a) Ta có : 64x² - (8x + y)² 

= (8x)² - (8x + y)² 

= (8x - 8x - y) (8x + 8x + y)

= -y(16x + y)

Bài 1:

a)\(64x^2-(8x+y)^2=-y\left(16x+y\right)\)

b)\((x+y+15)^2-2(x+y+15)+1\)

\(=\left(x+y+14\right)^2\)

c)\(8x^3+60x^2y+150xy^2+125y^3\)

\(=\left(2x+5y\right)^3\)

d)\(x^{16}-1\)

\(=\left(x-1\right)\left(x+1\right)\left(x^2+1\right)\left(x^4+1\right)\left(x^8+1\right)\)

Bài 2:

\(\left(n+7\right)^2-\left(n-5\right)^2\)

\(=\left(n+7+n+5\right)\left(n+7-\left(n+7\right)\right)\)

\(=24\left(n+1\right)\) chia hết 24

a) = (3x)^2 + 2.3x.5+ 5^2 = (3x+5)^2

b) = (2/3x)^2-(4y)^2=(2/3x-4y)(2/3x+4y)

c) = -(9x^4-12/5x^2y^2+4/25y^4) = -[(3x^2)^2 - 2.3x^2.2/5y^2 + (2/5y^2)^2]= -(3x^2-2/5y^2)^2

d) = (x-5)^2 -  4^2= (x-5+4)(x-5-4) = (x-1)(x-9)

e) = (2x)^3 + 3.(2x)^2.(5y) + 3.(2x).(5y)^2 + (5y)^3 = (2x+5y)^3

f) = (8x)^2 - (8a+b)^2 = (8x-8a-b)(8x+8a+b)

g) = (7x-4-2x-1)(7x-4+2x+1) = (5x-5)(9x-3) = 5(x-1).3(x-3)=15(x-1)(x-3)

h) = (x-y)(x+y)- 2(x+y) = (x+y)(x-y-2)

# Chúc bạn học tốt #

Cảm ơn bạn!

mình khỏi ghi đề nha, bạ đọc tự hiểu nha

a) (3x+5)²

b) \(\frac{2}{3}\).\(\left(\frac{2}{3}x^4-24y^2\right)\)

d) x(x-10)+9

e) 4x²(2x + 15y) + 25y²(6x + 5y)  

f) b(-16a+b)

g) 15x(5x-4+1)

câu còn lại bạn tự làm nha, lười quá!

h)