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

b: \(\left(x^2+4\right)^2-16x^2\)

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

\(=\left(x-2\right)^2\cdot\left(x+2\right)^2\)

c: \(x^5-x^4+x^3-x^2\)

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

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

Lời giải:

a. Bạn xem lại đề

b. \((x^2+4)^2-16x^2=(x^2+4)^2-(4x)^2=(x^2+4-4x)(x^2+4+4x)\)

\(=(x-2)^2(x+2)^2\)

c.

\(x^5-x^4+x^3-x^2=x^4(x-1)+x^2(x-1)=(x^4+x^2)(x-1)\)

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

a) 7x.(-y)+2(y-x)2

=>-7xy+4y-4x

b)(x^2+4)-16x^2

=>x^2+4-16x^2

=>-15x^2+4

c)x^5-x^4+x^3-x^2

=>x^4(x-1)+x^2(x-1)

=>(x^4+x^2)(x-1)

1/(x+2)² -(3x-1)²=(x+2+3x-1)(x+2-3x+1)=4x(-2x+3)=-8x²+12x

2/(x⁴+x²)(-2x³-2x)=x²(x²+1)-2x(x²+1)=(x²+1)(x²-2x)

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

 a) 3x2 – 7x + 2

\(=3x^2-6x-x+2\)

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

\(=3x\left(x-2\right)-\left(x-2\right)\)

\(=\left(x-2\right)\left(3x-1\right)\)

 b) a(x2 + 1) – x(a2 + 1)

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

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

.......?

a) Ta có: \(3x^2-7x+2\)

\(=3x^2-6x-x+2\)

\(=3x\left(x-2\right)-\left(x-2\right)\)

\(=\left(x-2\right)\left(3x-1\right)\)

b) Ta có: \(a\left(x^2+1\right)-x\left(a^2+1\right)\)

\(=x^2a+a-a^2x-x\)

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

\(=xa\left(x-a\right)-\left(x-a\right)\)

\(=\left(x-a\right)\left(xa-1\right)\)

c) Ta có: \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24\)

\(=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24\)

\(=\left(x^2+7x\right)^2+22\left(x^2+7x\right)+120-24\)

\(=\left(x^2+7x\right)^2+22\left(x^2+7x\right)+96\)

\(=\left(x^2+7x\right)^2+16\left(x^2+7x\right)+6\left(x^2+7x\right)+96\)

\(=\left(x^2+7x\right)\left(x^2+7x+16\right)+6\left(x^2+7x+16\right)\)

\(=\left(x^2+7x+16\right)\left(x^2+7x+6\right)\)

\(=\left(x^2+7x+16\right)\left(x+1\right)\left(x+6\right)\)

d) Ta có: \(\left(a+1\right)\left(a+3\right)\left(a+5\right)\left(a+7\right)+15\)

\(=\left(a^2+8a+7\right)\left(a^2+8a+15\right)+15\)

\(=\left(a^2+8a\right)^2+22\left(a^2+8a\right)+105+15\)

\(=\left(a^2+8a\right)^2+22\left(a^2+8a\right)+120\)

\(=\left(a^2+8a\right)^2+12\left(a^2+8a\right)+10\left(a^2+8a\right)+120\)

\(=\left(a^2+8a\right)\left(a^2+8a+12\right)+10\left(a^2+8a+12\right)\)

\(=\left(a^2+8a+12\right)\left(a^2+8a+10\right)\)

\(=\left(a+2\right)\left(a+6\right)\left(a^2+8a+10\right)\)

a,x(x+y)-5x-5y

=x(x+y)-5(x+y)

=(x+y)(x-5)

b,3x-5y-6ax+10ay

=(3x-6ax)-(5y-10ay)

=3x(1-2a)-5y(1-2a)

=(1-2a)(3x-5y)

c,a²-6a-b²+6b

=(a²-b²)-(6a-6b)

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

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

d,100a²-20a-2b-b²

=(100a²-b²)-(20a+2b)

=(10a-b)(10a+b)-2(10a+b)

=(10a+b)(10a-b-2)

e,36x²-12x+1-b²

=(36x²-12x+1)-b²

=(6x-1)²-b²

=(6x-1-b)(6x-1+b)

f,x²-z²+y²-2xy

=(x²-2xy+y²)-z²

=(x-y)²-z²

=(x-y-z)(x-y+z)

\(a,=\left(2a-1\right)\left(2a+1\right)\\ b,=\left(x-\sqrt{3}\right)\left(x+\sqrt{3}\right)\\ c,=\left(16-3x\right)\left(16+3x\right)\\ d,Sửa:-36x^2+24x-4=-4\left(9x^2-6x+1\right)=-4\left(3x-1\right)^2\)

\(a,=\left(2a-1\right)\left(2a+1\right)\\ b,=\left(x-\sqrt{3}\right)\left(x+\sqrt{3}\right)\\ c,=\left(16-3y\right)\left(16+3y\right)\)

a) \(=\left(6x\right)^2-2.6x.1+1=\left(6x-1\right)^2\)

b) \(=5xy\left(x^2+2x+1\right)=5xy\left(x+1\right)^2\)

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

d) \(=x\left(x+1\right)+7\left(x+1\right)=\left(x+1\right)\left(x+7\right)\)

b) \(25-x^2+14xy-49y^2\)

\(=25-\left(x^2-14xy+49y^2\right)\)

\(=25-\left[x^2-2\cdot7y\cdot x+\left(7y\right)^2\right]\)

\(=25-\left(x-7y\right)^2\)

\(=5^2-\left(x-7y\right)^2\)

\(=\left[5-\left(x-7y\right)\right]\left[5+\left(x-7y\right)\right]\)

\(=\left(5-x+7y\right)\left(5+x-7y\right)\)

c) \(x^5+x^4+1\)

\(=x^5+x^4+1+x^3-x^3\)

\(=\left(x^5+x^4+x^3\right)+\left(1-x^3\right)\)

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

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

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

b: 25-x^2+14xy-49y^2

=25-(x-7y)^2

=(5-x+7y)(5+x-7y)

c: =x^5+x^4+x^3+1-x^3

=x^3(x^2+x+1)+(1-x)(x^2+x+1)

=(x^2+x+1)(x^3+1-x)

\(\left(x^2+4x+8\right)^2+3x\left(x^2+4x+8\right)+2x^2=\left(x^2+4x+8+\dfrac{3}{2}x\right)^2-\dfrac{1}{4}x^2=\left(x^2+\dfrac{11}{2}x+8\right)^2-\left(\dfrac{1}{2}x\right)^2=\left(x^2+\dfrac{11}{2}x+8-\dfrac{1}{2}x\right)\left(x^2+\dfrac{11}{2}x+8+\dfrac{1}{2}x\right)=\left(x^2+5x+8\right)\left(x^2+6x+8\right)=\left(x+2\right)\left(x+4\right)\left(x^2+5x+8\right)\)

\(\left(x^2+4x+8\right)^2+3x\left(x^2+4x+8\right)+2x^2\)

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

\(=\left(x^2+4x+8\right)\left(x^2+5x+8\right)+2x\left(x^2+5x+8\right)\)

\(=\left(x^2+5x+8\right)\left(x+2\right)\left(x+4\right)\)