a)\(36-4a^2+20ab-25b^2=6^2-\left(4a^2-20ab+25b^2\right)\)
\(=6^2-\left[\left(2a\right)^2-2.2a.5b+\left(5b\right)^2\right]\)
\(=6^2-\left(2a-5b\right)^2\)
\(=\left(6-2a+5b\right)\left(6+2a-5b\right)\)
b)\(a^3+3a^2+3a+1-27b^3=\left(a+1\right)^3-\left(3b\right)^3\)(chỗ này mình sửa 27b2 thành 27b3 vì mình nghĩ nhầm đề)
\(=\left(a+1-3b\right)\left[\left(a+1\right)^2+\left(a+1\right)3b+\left(3b\right)^2\right]\)
\(=\left(a+1-3b\right)\left(a^2+2a+1+3ab+3b+9b^2\right)\)
c)\(x^3+3x^2+3x+1-3x^2-3x=\left(x+1\right)^3-3x\left(x+1\right)\)
\(=\left(x+1\right)\left[\left(x+1\right)^2-3x\right]\)
\(=\left(x+1\right)\left(x^2+2x+1-3x\right)\)
\(=\left(x+1\right)\left(x^2-x+1\right)\)
a) 36-4a2+20ab-25b2
= 6^2 - (4a^2 - 20xb + 25b^2)
= 6^2 - (2a - 5b)^2
= [6 - (2a - 5b)] [6 + (2a - 5b)]
= (6 - 2a + 5b) (6 + 2a -5b)
a) \(6^2-\left(\left(2a\right)^2-2.2a.5b+\left(5b\right)^2\right)\)
\(=6^2-\left(2a-5b\right)^2\)
\(=\left(6-2a+5b\right)\left(6+2a-5b\right)\)
b) \(=\left(a+1\right)^3-\left(3b\right)^3\)
\(=\left(a+1-3b\right)\left(\left(a+1\right)^2+3b\left(a+1\right)+\left(3b\right)^2\right)\)
\(=\left(a+1-3b\right)\left(a^2+2a+1+3ab+3b+9b^2\right)\)
c) \(=\left(x+1\right)^3-3x\left(x+1\right)\)
\(=\left(x+1\right)\left(\left(x+1\right)^2-3x\right)\)
\(=\left(x+1\right)\left(x^2+2x+1-3x\right)\)
\(=\left(x+1\right)\left(x^2-x+1\right)\)
