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A = (x - 1)(x + 3) - (x - 2)(5x - 4)
A = x2 + 2x - 3 - 5x2 + 14x - 8
A = -4x2 + 16x - 11
B = (3a - 2b)(9a2 + 6ab - 4b2)
B = 27a3 + 18a2b - 12ab2 - 18a2b - 12ab2 + 8b3
B = 27a3 -24ab2 + 8b3
C = (x - 1)(x + 1) - (2x - 3)(4 - 5x)
C = x2 - 1 - 8x + 10x + 12 - 15x
C = x2 - 13x + 11
Làm trc cho 2 câu cuối
c) \(a^2-b^2-4a+4b\)
\(=\left(a+b\right)\left(a-b\right)-4\left(a-b\right)\)
\(=\left(a-b\right)\left[\left(a+b\right)-4\right]\)
d) \(a^2+2ab+b^2-2a-2b+1\)
\(=\left(a+b\right)^2-2\left(a+b\right)+1\)
\(=\left(a+b\right)\left[\left(a+b\right)-2\right]+1\)
cách khác:
\(B=\frac{3a-2b}{2a+5}+\frac{3b-a}{b-5}\)
\(=\frac{3a-2b}{2a+a-2b}+\frac{3b-a}{b-a+2b}\) (thay 5 = a - 2b)
\(=\frac{3a-2b}{3a-2b}+\frac{3b-a}{3b-a}\)
\(=1+1=2\)
Biết a - 2b = 5 tính giá trị biểu thức:
\(B=\frac{3a-2b}{2a+5}+\frac{3b-a}{b-5}\)
\(=\frac{2a+\left(a-2b\right)}{2a+5}+\frac{3b-a}{b-5}\)
\(=\frac{2a+5}{2a+5}+\frac{b-5}{b-5}\)
\(=1+1=2\)
Vậy B = 2
\(A=\frac{9a^5-ab^4-18a^4b+2b^5}{3a^2b^2+ab^4-6a^2b^3-2b^5}\)
\(=\frac{a\left(9a^4-b^4\right)-2b\left(9a^4-b^4\right)}{ab^2\left(3a^2+b^2\right)-2b^3\left(3a^2+b^2\right)}\)
\(=\frac{\left(9a^4-b^4\right)\left(a-2b\right)}{\left(3a^2+b^2\right)\left(ab^2-2b^3\right)}\)
\(=\frac{\left(3a^2-b^2\right)\left(3a^2+b^2\right)\left(a-2b\right)}{\left(3a^2+b^2\right)b^2\left(a-2b\right)}\)
\(=\frac{3a^2-b^2}{b^2}\)
\(=3.\left(\frac{a}{b}\right)^2-1=3.\left(\frac{2}{3}\right)^2-1=\frac{1}{3}\)