bài 4 : Thu gọn :
a, ( x-2 ) . ( x+2) - ( x-3 ) . ( x+ 1)
= x² + 2x - 2x - 4 - (x² + x - 3x - 3)
= x² - 4 - x² - x + 3x + 3
= 2x - 1
b, ( 2x+1 ) . ( 2x-1 ) - ( 3x-1 ) . ( 3x-1 ) + ( 2x+1 ) . ( 3x-1 )
= 4x² - 1 - (3x - 1)² + 6x² - 2x + 3x - 1
= 4x² - 1 - (9x² - 6x + 1) + 6x² - 2x + 3x - 1
= 4x² - 1 - 9x² + 6x - 1 + 6x² - 2x + 3x - 1
= x² + 7x - 3
c, ( x+2 ) . ( x-2 ) - ( x+3 ) . ( x+3 )
= x² - 4 - (x + 3)²
= x² - 4 - (x² + 6x + 9)
= x² - 4 - x² - 6x - 9
= -6x - 13
d, ( x ² - y ² ) . ( 6x+3y ) - ( x-y ) . ( 2x+y )
= 6x³ + 3x²y - 6xy² - 3y³ - (2x² + xy - 2xy - y²)
= 6x³ + 3x²y - 6xy² - 3y³ - 2x² - xy + 2xy + y²
= 6x³ + 3x²y - 6xy² - 3y³ - 2x² + xy + y²
bài 5 : tính (Áp dụng hằng đẳng thức)
a, ( a+b)²
= a² + 2ab + b²
b, ( a-b )²
= a² - 2ab + b²
c, ( a+b ) . ( a-b )
= a² - b²