bài 4 : Thu gọn :
a, ( x-2 ) . ( x+2) – ( x-3 ) . ( x+ 1)
b, ( 2x+1 ) . ( 2x-1 ) – ( 3x-1 ) . ( 3x-1 ) + ( 2x+1 ) . ( 3x-1 )
c, ( x+2 ) . ( x-2 ) – ( x+3 ) . ( x+3 )
d, ( x ² – y ² ) . ( 6x+3y ) – ( x-y ) . ( 2x+y )
bài 5 : tính
a, ( a+b) ²
b, ( a-b ) ²
c, ( a+b ) . ( a-b )
GIÚP MIK VỚI AK , CẢM ƠN !!!!!!!!!!!!!!!!!!!!!!!!!!!!
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
Đáp án:
Giải thích các bước giải:
4/ a/ $(x-2)(x+2)-(x-3)(x+1)$
$=x^2-4-(x^2-3x+x-3)$
$=x^2-4-x^2+3x-x+3$
$=2x-1$
b/ $(2x+1)(2x-1)-(3x-1)(3x-1)+(2x+1)(3x-1)$
$=4x^2-1-(3x-1)^2+(6x^2+3x-2x-1)$
$=4x^2-1-(9x^2-6x+1)+6x^2+x-1$
$=4x^2-1-9x^2+6x-1+6x^2+x-1$
$=x^2+7x-2$
c/ $(x+2)(x-2)-(x+3)(x+3)$
$=x^2-4-(x+3)^2$
$=x^2-4-(x^2+6x+9)$
$=x^2-4-x^2-6x-9$
$=-6x-13$
d/ $(x^2-y^2)(6x+3y)-(x-y)(2x+y)$
$=3(x-y)(x+y)(2x+y)-(x-y)(2x+y)$
$=(x-y)(2x+y)(3x+3y-1)$
5/ a/ $(a+b)^2=a^2+2ab+b^2$
b/ $(a-b)^2=a^2-2ab+b^2$
c/ $(a+b)(a-b)=a^2-b^2$
Chúc bạn học tốt !!