Question

1) Rut gon cac bieu thuc sau :

a) (x-3)(x²+3x+ 9)-(54+x³)

b) (3x+y)(9x²-3xy +y²)-(3x-y)(9x²+3xy+y²)

2) Chung minh rang:

a) a³+b³= (a+b)³ -3ab(a+b)

b) a³-b³=(a-b)³ +3ab(a-b)

Ap dung : Tinh a³+b³ biet ab=12va a+b =-7

nhah nha mk dang can rat gap

Answer 1

Tham khảo nha \(\)

1. Rút gọn:

a/ \(\left(x-3\right)\left(x^2+3x+9\right)+\left(54+x^3\right)\)

= \(x^3+3x^2+9x-3x^2-9x-27+54+x^3\)

= \(2x^3+27\)

b/ \(\left(3x+y\right)\left(9x^2-3xy+y^2\right)-\left(3x-y\right)\left(9x^2+3xy+y^2\right)\)

\(=27x^3-9x^2y+3xy^2+9x^2y-3xy^2+y^3-27x^3+9x^2y+3xy^2-9x^2y-3xy^2-y^3\)

\(=\left(27x^3-y^3\right)-\left(27x^3+y^3\right)\)

\(=27x^3-y^3-27x^3-y^3=-2y^3\)

2.Chứng minh rằng:

a/ \(a^3+b^3=\left(a+b\right)^3-3ab\left(a+b\right)\)

Xét VP có:

\(=a^3+3a^2b+3ab^2+b^3-3a^2b-3ab^2\)

\(=a^3+b^3\)

=> VT=VP

=> \(a^3+b^3=\left(a+b\right)^3-3ab\left(a+b\right)\)

b/ \(a^3-b^3=\left(a-b\right)^3+3ab\left(a-b\right)\)

Xét VP có:

\(=a^3-3a^2b+3ab^2-b^3+3a^2b-3ab^2\)

\(=a^3-b^3\)

=> VT=VP

=> \(a^3-b^3=\left(a-b\right)^3+3ab\left(a-b\right)\)

Chúc bạn học tốt ♥

Answer 2

2

a, ta có (a+b)³-3ab(a+b)

= a³+3a²b+3ab²+b³-3a²b-2ab²

= a³+b³(đpcm)

b, ta có (a-b)³ +3ab(a+b)

= a³ -3a²b+3ab²-b³+3a²b -2ab²

= a³-b³ (đpcm)

áp dụng

a³+b³=(a+b)³-3ab(a+b)

=(-5)³-3.6(-5)

=-35