a,\(8x^2-8xy+2x=2x\left(4x-8y+1\right)\)

b,\(\left(x^2+2x\right)\left(x^2+4x+3\right)-24=x\left(x+2\right)\left(x+1\right)\left(x+3\right)-24\)

\(=\left(x^2+3x\right)\left(x^2+3x+2\right)-24=\left(t+1\right)\left(t-1\right)-24=t^2-5^2=\left(t+5\right)\left(t-5\right)\)

\(=\left(x^2+3x+6\right)\left(x^2+3x-4\right)\)( đặt t = x² + 3x + 1 )

Các ý đã phân tích triệt để : a) , b) , c) , d) , e) , f) , g) , h) , l)

Các ý còn lại chưa phân tích triệt để , và mình sẽ phân tích luôn ^^

i) 3x + 9 + 4x² + 12x = ( 3x + 9 ) + ( 4x² + 12x ) = 3( x + 3 ) + 4x( x + 3 ) = ( x + 3 )( 4x + 3 )

k) [ ( x + 1 ) + 5 ][ ( x + 1 ) - 5 ] = ( x + 1 + 5 )( x + 1 - 5 ) = ( x + 6 )( x - 4 )

m) 6x² + 6xy - 7x - 7y = ( 6x² + 6xy ) - ( 7x + 7y ) = 6x( x + y ) - 7( x + y ) = ( x + y )( 6x - 7 )

7x² - 7x( x - 3 ) = x + 2

⇔ 7x² - 7x² + 21x = x + 2

⇔ 21x = x + 2

⇔ 21x - x = 2

⇔ 20x = 2

⇔ x = 2/20 = 1/10

làm nhan hộ với 8 h mink phải nộp rồi

\(ax^2+bx^2-bx-ax+cx^2-cx\)

\(=\left(ax^2-ax\right)+\left(bx^2-bx\right)+\left(cx^2-cx\right)\)

\(=ax\left(x-1\right)+bx\left(x-1\right)+cx\left(x-1\right)\)

\(=\left(x-1\right)\left(ax+bx+cx\right)\)

\(=x\left(x-1\right)\left(a+b+c\right)\)

ax²+bx²-bx-ax+cx²-cx

= (ax² - ax ) + (bx² -bx ) + ( cx² - cx )

= a(x) + b(x) + c(x)

= (x)(a+b+c)

a⁴ + 4 = (a²)² + 4 = (a²)² + 4a² + 4 - 4a²

                             = (a² + 2)² - (2a)²

                             = (a² - 2a + 2)(a² + 2a + 2)

a⁴+4=

a⁴+ 4a²+4-4a²=(a²+2)²-4a²=(a²+2+2x).(a²+2-2x)

khó vaiz

thế mới hỏi

Ta có A = x² - 6x + 10

= x² - 6x + 9 + 1 

= (x - 3)² + 1 \(\ge\)1 

Dấu "=" xảy ra <=>x - 3 = 0 => x = 3

Vậy Min A = 1 <=> x = 3

\(A=2x^3+3\left(x-1\right)\left(x+1\right)-5x\left(x+1\right)\)

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

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

\(=2x^3-2x^2-5x-3\)

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

\(=125-150x+60x^2-8x^3-\left(25-9x^2\right)\)

\(=125-150x+60x^2-8x^3-25+9x^2\)

\(=100-15x+69x^2-8x^3\)

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

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

\(=\left(x+2\right).5x\)

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

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

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

\(E=\left(x-2\right)^3-x\left(x+1\right)\left(x-1\right)+6x\left(x-3\right)\)

\(=x^3-6x^2+12x-8+x\left(x^2-1\right)+6x^2-18x\)

\(=x^3-6x^2+12x-8+x^3-x+6x^2-18x\)

\(=-7x-8\)

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

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

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

\(=-3\)