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 ♥
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
