Question

3 Rút gon đa thức :

a) (4n^2-6nm+9m^2)(2n+3m) ; b) (7+2b)(4b^2-4b+49)

c) (25a^2+10ab+4b^2)(5a-2b) ; d) (x^2+x+2)(x^2-x-2)

Answer 1

a) \(\left(4n^2-6nm+9m^2\right)\left(2n+3m\right)\)

\(=\left(2n+3m\right)\left[\left(2n\right)^2-2n.3m+\left(3m\right)^2\right]\)

\(=\left(2n\right)^3+\left(3m\right)^3\)

\(=8n^3+27m^3\)

b) Sửa đề \(\left(7+2b\right)\left(4b^2-14b+49\right)\)

\(=\left(7+2b\right)\left[\left(2b\right)^2-2b.7+7^2\right]\)

\(=7^3+\left(2b\right)^3\)

\(=343+8b^3\)

c) \(\left(25a^2+10ab+4b^2\right)\left(5a-2b\right)\)

\(=\left(5a-2b\right)\left[\left(5a\right)^2+5a.2b+\left(2b\right)^2\right]\)

\(=\left(5a\right)^3-\left(2b\right)^3\)

\(=125a^3-8b^3\)

d) \(\left(x^2+x+2\right)\left(x^2-x-2\right)\)

\(=\left[x^2+\left(x+2\right)\right]\left[x^2-\left(x+2\right)\right]\)

\(=x^4-\left(x+2\right)^2\)