a) \(2a^2x-5by-5a^2y+2by\) 

 \(=3\left(\frac{2}{3}a^2x-\frac{5}{3}a^2y\right)-3by\) 

\(=3\left(\frac{2}{3}a^2x-\frac{5}{3}a^2y-by\right)\) 

\(25a^2b^2-4x^2+4x-1\)

\(=\left(5ab\right)^2-\left(4x^2-4x+1\right)\)

\(=\left(5ab\right)^2-\left[\left(2x\right)^2-2.2x.1+1^2\right]\)

\(=\left(5ab\right)^2-\left(2x-1\right)^2\)

\(=\left(5ab-2x+1\right)\left(5ab+2x-1\right)\)

bn có chép sai dấu các hạng tử ko vậy ,mk nghĩ bn chép sai dấu của hạng tử 1

\(=\left(4x^2-4xy+y^2\right)-\left(25a^2-10a+1\right)=\left(2x-y\right)^2-\left(5a-1\right)^2\)

\(=\left(2x-y-5a+1\right)\left(2x-y+5a-1\right)\)

\(=\left(4x^2-4xy+y^2\right)-\left(25a^2-10a+1\right)\\ =\left(2x-y\right)^2-\left(5a-1\right)^2\\ =\left(2x-y-5a+1\right)\left(2x-y+5a-1\right)\)

5.

\(4x^5y^2+8x^4y^3+4x^3y^4=4x^3y^2(x^2+2xy+y^2)\)

\(=4x^3y^2(x+y)^2\)

9.

\(4x^5y^2+16x^4y^2-6x^3y^2=2x^3y^2(2x^2+4x-3)\)

13.

\(-3x^4y+6x^3y-3x^2y=-3x^2y(x^2-2x+1)=-3x^2y(x-1)^2\)

17.

\(8x^3-8x^2y+2xy^2=2x(4x^2-4xy+y^2)\)

\(=2x[(2x)^2-2.2x.y+y^2]=2x(2x-y)^2\)

21.

\((a^2+4)^2-16a^2b^2=(a^2+4)^2-(4ab)^2\)

\(=(a^2+4-4ab)(a^2+4+4ab)\)

25.

\(100a^2-(a^2+25)^2=(10a)^2-(a^2+25)^2\)

\(=(10a-a^2-25)(10a+a^2+25)\)

\(=-(a^2-10a+25)(a^2+10a+25)=-(a-5)^2(a+5)^2\)

29.

\(25a^2b^2-4x^2+4x-1=25a^2b^2-(4x^2-4x+1)\)

\(=(5ab)^2-(2x-1)^2=(5ab-2x+1)(5ab+2x-1)\)

33.

\(1-2m+m^2-x^2-4x-4=(m^2-2m+1)-(x^2+4x+4)\)

\(=(m-1)^2-(x+2)^2=[(m-1)-(x+2)][(m-1)+(x+2)]\)

\(=(m-x-3)(m+x+1)\)

37.

\(ax^2+bx^2+2xy(a+b)+ay^2+by^2\)

\(=x^2(a+b)+2xy(a+b)+y^2(a+b)\)

\(=(a+b)(x^2+2xy+y^2)=(a+b)(x+y)^2\)

41.

\(5a^2-5=5(a^2-1)=5(a^2-1^2)=5(a-1)(a+1)\)

\(4x^2-4xy+y-25a^2+10a-136\)

\(\text{Phân tích thành nhân tử}\)

\(-\left(4xy-y-4x^2+25a^2-10a+136\right)\)

k nhé !

a. y⁴ - 14y² + 49

Gọi y² là t, ta có:

t² - 14t + 49

<=> t² - 14t + 7²

<=> (t - 7)²

Thay x² = t

<=> (x² - 7)²

b. \(\dfrac{1}{4}-x^2\)

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

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

c. x⁴ - 16

<=> (x²)² - 4²

<=> (x² - 4)(x² + 4)

d. x² - 9

<=> x² - 3²

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

Bài 1: 

a: \(y^2-14y^2+49=\left(y-7\right)^2\)

b: \(\dfrac{1}{4}-x^2=\left(\dfrac{1}{2}-x\right)\left(\dfrac{1}{2}+x\right)\)

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

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

Sai đề

Sửa đề: \(4x^2-4xy+y^2-25a^2+10a-1\)

\(=\left(2x-y\right)^2-\left(5a-1\right)^2\)

\(=\left(2x-y-5a+1\right)\left(2x-y+5a-1\right)\)

Mình làm và sửa đề đúng luôn nhé !

1) \(36x^2-a^2+10a-25\)

\(=\left(6x\right)^2-\left(a^2-10a+25\right)\)

\(=\left(6x\right)^2-\left(a-5\right)^2\)

\(=\left(6x-a+5\right)\left(6x+a-5\right)\)

2) \(4x^2-4xy+y^2-25a^2+10a-1\)

\(=\left(2x-y\right)^2-\left(5a-1\right)^2\)

\(=\left(2x-y-5a+1\right)\left(2x-y+5a-1\right)\)

3) \(m^2-6m+9-x^2+4xy-4y^2\)

\(=\left(m-3\right)^2-\left(x-2y\right)^2\)

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

a: Ta có: \(\sqrt{9x-54}-\sqrt{4x-24}=2\)

\(\Leftrightarrow3\sqrt{x-6}-2\sqrt{x-6}=2\)

\(\Leftrightarrow x-6=4\)

hay x=10

b: Ta có: \(\sqrt{4x^2+4x+1}=7\)

\(\Leftrightarrow\left|2x+1\right|=7\)

\(\Leftrightarrow\left[{}\begin{matrix}2x+1=7\\2x+1=-7\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=6\\2x=-8\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-4\end{matrix}\right.\)