a) \(x^2+12x+35\)

\(=x^2+5x+7x+35\)

\(=\left(x^2+5x\right)+\left(7x+35\right)\)

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

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

b)\(x^2-x-56\)

\(=x^2+7x-8x-56\)

\(=\left(x^2+7x\right)-\left(8x+56\right)\)

\(=x\left(x+7\right)-8\left(x+7\right)\)

\(=\left(x+7\right)\left(x-8\right)\)

c)\(5x^2-x-4\)

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

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

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

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

TL:

a)\(x^2+5x+7x+35\) 

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

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

b) \(x^2-x-56\)

  =\(x^2+7x-8x-56\) 

=\(x\left(x+7\right)-8\left(x+7\right)\) 

=\(\left(x-8\right)\left(x+7\right)\) 

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

=\(\left(2x^2+1\right)^2-4x^2\) 

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

.......................(tự lm)

hc tốt

\(4\times^4+81\)

\(=\left(2\times^2\right)^2+36\times^2+9^2-36\times^2\)

\(=\left(2\times^2+9\right)^2-36\times^2\)

\(=\left(2\times^2+9+36\times\right)\left(2\times^2+9-36\times\right)\)

a) x² - x - 56

b) x^4 + 64

c) 4x^4 + 81

d) x².+ 12x + 35

e) 5x² - x - 4

g) 4x^4 + 1

h) 64x^4 + y^4

a)\(x^2-x-56\)

\(=x^2-8x+7x-56\)

\(=\left(x^2-8x\right)+\left(7x-56\right)\)

\(=x\left(x-8\right)+7\left(x-8\right)\)

\(=\left(x-8\right)\left(x+7\right)\)

b)\(x^4+64\)

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

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

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

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

c)\(4x^4+81\)

\(=\left(2x^2\right)^2+9^2\)

\(=\left(2x^2\right)^2+36x^2+9^2-36x^2\)

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

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

d)\(x^2+12x+35\)

\(=x^2+5x+7x+35\)

\(=\left(x^2+5x\right)+\left(7x+35\right)\)

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

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

e)\(5x^2-x-4\)

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

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

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

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

g)\(4x^4+1\)

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

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

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

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

h)\(64x^4+y^4\)

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

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

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

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

a) x²-x-56

=x²+7x-8x-56

=x(x+7)-8(x+7)

=(x-8)(x+7)

d) x²+12x+35

=x²+7x+5x+7

=x(x+7)+5(x+7)

=(x+5)(x+7)

e)5x²-x-4

=5x²+4x-5x-4

=x(5x+4)-1(5x+4)

=(x-1)(5x+4)

a) x²-7x+6= (x-6)(x-1)

câu c,e , g tương tự nha bạn

b) x⁴+64= x⁴+16x²+64-16x²=(x²+8)²-16x²=(x²+8-4x)(x²+8+4x)

các câu còn lại cũng tượng tự nha bạn

\(a,x^2-7x+6=x^2-6x-x+6\)

\(=x\left(x-6\right)-\left(x-6\right)=\left(x-1\right)\left(x-6\right)\)

\(b,x^4+64=\left(x^4+16x^2+64\right)-16x^2\)

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

\(c,x^2+12x+35=x^2+5x+7x+35\)

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

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

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

\(e,x^2-x-56=x^2-8x+7x-56\)

\(=x\left(x-8\right)+7\left(x-8\right)=\left(x+7\right)\left(x-8\right)\)

\(f,4x^2+81=\left(4x^4+36x^2+81\right)-36x^2\)

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

\(g,5x^2-x-4=5x^2-5x+4x-4\)

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

\(h,64x^4+y^4=\left(64x^4+16x^2y^2+y^4\right)-16x^2y^2\)

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

a) \(x^2-7x+6=x^2-6x-x+6\)

\(=x\left(x-6\right)-\left(x-6\right)\)

\(=\left(x-6\right)\left(x-1\right)\)

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

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

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

c) \(x^2+12x+35=x^2+5x+7x+35\)

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

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

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

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

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

e) \(x^2-x-56=x^2+7x-8x-56\)

\(=x\left(x+7\right)-8\left(x+7\right)\)

\(=\left(x+7\right)\left(x-8\right)\)

f) \(4x^4+81=4x^4+81+36x^2-36x^2\)

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

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

g) \(5x^2-x-4=5x^2+4x-5x-4\)

\(=x\left(5x+4\right)-\left(5x+4\right)\)

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

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

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

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

a) x¹² + 4 = x¹² + 4x⁶ + 4 - 4x⁶ = (x⁶ + 2)² - (2x³)² 

= (x⁶ - 2x³ + 2)(x⁶ + 2x³ + 2)

b) 4x⁸ + 1 = 4x⁸ + 4x⁴  + 1 - 4x⁴ = (2x⁴ + 1)² - (2x²)² 

= (2x⁴ + 2x² + 1)(2x⁴ - 2x²  + 1)

c) x⁷ + x⁵ - 1 = x⁷ - x + x⁵ + x² - (x² - x  + 1) = x(x⁶ - 1) + x²(x³ + 1) - (x² - x + 1)

= x(x³ - 1)(x³ + 1) + x²(x + 1)(x² - x + 1) - (x2 - x + 1)

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

= (x⁵ + x⁴ - x² - x + x³ + x² - 1)(x² -x + 1)

= (x⁵ + x⁴ + x³ - x - 1)(x² - x + 1)

d) x⁷ + x⁵ + 1 = x⁷ - x + x⁵ - x² + (x² + x + 1)

= x(x³ - 1)((x³ + 1) + x²(x³ - 1) + (x² + x + 1)

= (x⁴ + x)(x  - 1)(x² + x + 1) + x²(x - 1)((x² + x + 1) + (x² + x + 1)

= (x² + x + 1)(x⁵ - x⁴ + x² - x + x³ - x² + 1)

= (x² + x + 1)(x⁵ - x⁴ + x³ - x + 1)

tự làm

1.A

2.C

3.B

4.C

a

c

b

c

(x-1)y^2-4(x-1)y