\(ta\)\(có\)\(a^5+1=a^5+a^4-a^4-a^3+a^3+a^2-a^2+1\)

                                 \(=a^4\left(a+1\right)-a^3\left(a+1\right)+a^2\left(a+1\right)+\left(-a+1\right)\left(a+1\right)\)

                               \(=\left(a+1\right)\left(a^4-a^3+a^2-a+1\right)\)

a) Áp dụng hằng đằng thức hiệu của 2 bình phương ta có

\(x^2-7=x^2-\left(\sqrt{7}\right)^2=\left(x-\sqrt{7}\right)\left(x+\sqrt{7}\right)\)

                                                       Bài giải

\(a,\text{ }x^2-7=x^2-\left(\sqrt{7}\right)^2=\left(x-\sqrt{7}\right)\left(x+\sqrt{7}\right)\)

\(b,\text{ }4x-5=\left(2x\right)^2-\left(\sqrt{5}\right)^2=\left(2x-\sqrt{5}\right)\left(2x+\sqrt{5}\right)\)

\(x^2-7=x^2-\sqrt{7}^2=\left(x-\sqrt{7}\right)\left(x+\sqrt{7}\right)\)

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

Xin chúc mừng!Bạn đã đưa ra 1 câu hỏi mà chẳng ai muốn trả lời

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

x² - 2xy - x² + 4y²
= ( x² - x² ) - ( 2xy - 4y² )
= - 2y ( x - 2y )

1) Có 3 = (2² - 1)

=> BT = (2² - 1)(2² + 1)(2⁴ + 1)(2⁸ + 1)(2¹⁶ +1)

           = (2⁴ - 1)(2⁴ + 1)(2⁸ + 1)(2¹⁶ +1)

           = (2⁸ - 1)(2⁸ + 1)(2¹⁶ +1)

           = (2¹⁶ - 1)(2¹⁶ +1)

           = 2³² - 1

\(x^2-7x+12=x^2-3x-4x+12=x\left(x-3\right)-4\left(x-3\right)=\left(x-3\right)\left(x-4\right)\)

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

\(x^2+3x-18=x^2-3x+6x-18=x\left(x-3\right)+6\left(x-3\right)=\left(x-3\right)\left(x+6\right)\)

a,x²-7x+12=(x-4)(x-3)

b,3x²+13x-10=(3x-2)(x+5)

c,x²-2x-3=(x-3)(x+1)

d,x²+3x-18=(x-3)(x+6)

a. \(x^2-7x+12=x^2-3x-4x+12=x\left(x-3\right)-4\left(x-3\right)=\left(x-3\right)\left(x-4\right)\)

b. \(3x^2+13x-10=3x^2+15x-2x-10=3x\left(x+5\right)-2\left(x+5\right)=\left(x+5\right)\left(3x-2\right)\)

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

x²( x + 1 )² + 2x² + 2x - 8

= [ x( x + 1 ) ]² + 2( x² + x ) - 8

= ( x² + x )² + 2( x² + x ) - 8 (*)

Đặt a = x² + x

(*) = a² + 2a - 8

= a² - 2a + 4a - 8

= a( a - 2 ) + 4( a - 2 ) 

= ( a - 2 )( a + 4 )

= ( x² + x - 2 )( x² + x + 4 )

= ( x² - x + 2x - 2 )( x² + x + 4 )

= [ x( x - 1 ) + 2( x - 1 ) ]( x² + x + 4 )

= ( x - 1 )( x + 2 )( x² + x + 4 )

ta co

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

=\(\left(x\left(x+1\right)\right)^2+2x\left(x+1\right)+1-9\)

=\(\left(x^2+x+1\right)^2-9\)

=\(\left(x^2+x-8\right)\left(x^2+x+10\right)\)

=\(\left(x^2+2x\frac{1}{2}+\frac{1}{4}-\frac{33}{4}\right)\left(x^2+x+10\right)\)

=\(\left(\left(x+\frac{1}{2}\right)^2-\frac{33}{4}\right)\left(x^2+x+10\right)\)

=\(\left(x+\frac{1}{2}-\sqrt{\frac{33}{4}}\right)\left(x+\frac{1}{2}+\sqrt{\frac{33}{4}}\right)\left(x^2+x+10\right)\)

mik xin lỗi

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

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

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