d) \(3a^2-6ab+3b^2-12x^2\)

\(=3\left(a^2-2ab+b^2-4x^2\right)\)

\(=3\left[\left(a^2-2ab+b^2\right)-\left(2x\right)^2\right]\)

\(=3\left[\left(a-b\right)^2-\left(2x\right)^2\right]\)

\(=3\left(a-b-2x\right)\left(a-b+2x\right)\)

b) \(x^2+3cd\left(2-3cd\right)-10xy-1+25y^2\)

\(=\left(x^2-10xy+25y^2\right)+2.3cd-\left(3cd\right)^2-1\)

\(=\left(x-5y\right)^2-\left[\left(3cd\right)^2-2.3cd+1\right]\)

\(=\left(x-5y\right)^2-\left(3cd-1\right)^2\)

\(=\left[\left(x-5y\right)-\left(3cd-1\right)\right]\left[\left(x-5y\right)+\left(3cd-1\right)\right]\)

\(=\left(x-5y-3cd+1\right)\left(x-5y+3cd-1\right)\)

a) \(x^2-2xy+y^2-m^2+2mn-n^2\)

\(=\left(x^2-2xy+y^2\right)-\left(m^2-2mn+n^2\right)\)

\(=\left(x-y\right)^2-\left(m-n\right)^2\)

\(=\left[\left(x-y\right)-\left(m-n\right)\right]\left[\left(x-y\right)+\left(m-n\right)\right]\)

\(=\left(x-y-m+n\right)\left(x-y+m-n\right)\)

Tổng số tấn gạo sau khi nhập vào ở cả hai kho:

\(147+13+21=181\) (tấn)

Số tấn gạo ở kho thứ nhất lúc đầu:

\(\left(181+5\right):2-13=80\) (tấn)

Số tấn gạo ở kho thứ hai lúc đầu:

\(147-80=67\) (tấn)

Mỗi thùng dầu nặng số kg là:

\(0,76\times45,75+4,5=39,27\left(kg\right)\)

128 thùng dầu hỏa cân nặng:

\(39,27\times128=5026,56\left(kg\right)=50,2656\) (tạ)

d) \(\left(a+b\right)^3-\left(a-b\right)^3\)

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

\(=\left(a+b-a+b\right)\left(a^2+2ab+b^2+a^2-b^2+a^2-2ab+b^2\right)\)

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

c) \(27x^3-a^3b^3\)

\(=\left(3x\right)^3-\left(ab\right)^3\)

\(=\left(3x-ab\right)\left[\left(3x\right)^2+3xab+\left(ab\right)^2\right]\)

\(=\left(3x-ab\right)\left(9x^2+3xab+a^2b^2\right)\)

b) \(100-\left(3x-y\right)^2\)

\(=10^2-\left(3x-y\right)^2\)

\(=\left[10-\left(3x-y\right)\right].\left[10+\left(3x-y\right)\right]\)

\(=\left(10-3x+y\right)\left(10+3x-y\right)\)

a) \(a^2y^2+b^2x^2-2abxy\)

\(=\left(ay\right)^2-2aybx+\left(bx\right)^2\)

\(=\left(ay-bx\right)^2\)

Chọn D