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a) \(9\left(a+b\right)^2-4\left(a-2b\right)^2\)
\(=\left(3a+3b\right)^2-\left(2a-4b\right)^2\)
\(=\left(3a+3b-2a+4b\right)\left(3a+3b+2a-4b\right)\)
\(=\left(a+7b\right)\left(5a-b\right)\)
b) \(9x^6-12x^7+4x^8\)
\(=x^6\left(9-12x+4x^2\right)\)
\(=x^6\left(2x-3\right)^2\)
c) \(8x^6-27y^3\)
\(=\left(2x^2\right)^3-\left(3y\right)^3\)
\(=\left(2x^2-3y\right)\left(4x^4+6x^2y+9y^2\right)\)
d) \(\frac{1}{64}x^6-125y^3\)
\(=\left(\frac{1}{4}x^2\right)^3-\left(5y\right)^3\)
\(=\left(\frac{1}{4}x^2-5y\right)\left(\frac{1}{16}x^4+\frac{5}{6}xy+25y^2\right)\)
mk ghi đáp án, ko phân tích đc thì IB mk
a) \(x^2+6xy+9y^2=\left(x+3y\right)^2\)
b) \(4a^4-4a^2b^2+b^4=\left(2a^2-b^2\right)^2\)
c) \(x^6+y^2-2x^3y=\left(x^3-y\right)^2\)
d) \(\left(x+y\right)^3-\left(x-y\right)^3=2y\left(3x^2+y^2\right)\)
e) \(25x^4-10x^2y^2+y^4=\left(5x^2-y^2\right)^2\)
f) \(-a^2-2a-1=-\left(a+1\right)^2\)
g) \(27b^3-8a^3=\left(3b-2a\right)\left(9b^2+6ab+4a^2\right)\)
h) \(x^3+9x^2y+27xy^2+27y^3=\left(x+3y\right)^3\)
i) \(16x^2-9\left(x+y\right)^2=\left(x-3y\right)\left(7x+3y\right)\)
a) \(4x^4+4x^3-x^2-x=4x^3\left(x+1\right)-x\left(x+1\right)\)
\(=\left(4x^3-x\right)\left(x+1\right)=x\left(4x^2-1\right)\left(x+1\right)\)
\(=x\left\{\left(2x\right)^2-1\right\}\left(x+1\right)=x\left(2x-1\right)\left(2x+1\right) \left(x+1\right)\)
c) \(x^4-4x^3+8x^2-16x+16=x^4+8x^2+16-\left(4x^3+16x\right)\)
\(=\left(x^2+4\right)^2-4x\left(x^2+4\right)=\left(x^2-4x+4\right)\left(x^2+4\right)=\left(x-2\right)^2\left(x^2+4\right)\)
b) \(x^6-x^4-9x^3+9x^2=x^4\left(x^2-1\right)-\left(9x^3-9x^2\right)\)
\(=x^4\left(x-1\right)\left(x+1\right)-9x^2\left(x-1\right)\)
\(=\left(x^5+x^4-9x^2\right)\left(x-1\right)=\left(x-1\right)x^2\left(x^3+x^2-9\right)\)
a,
=\(\left(a^2\right)^2-\left(2b\right)^2\)
=\(\left(a^2-2b\right)\left(a^2+2b\right)\)
= \(\left(\left(a-\sqrt{2b}\right)\left(a+\sqrt{2b}\right)\right)\left(a^2+2b\right)\)
c,
=\(4x^4+20x^2+25\)
=\(\left(2x^2\right)^2+2.2x^2.5+5^2\)
=\(\left(2x^2+5\right)^2\)
d,
=\(8x^6-27y^3\)
= \(\left(2x^2\right)^3-\left(3y\right)^3\)
= \(\left(2x^2-3y\right)\left(4x^4+6x^2y+9y^2\right)\)
Câu b đề ghi ko rõ lắm
Ta có : x3 - 7x + 6
= x3 - x - 6x + 6
= x(x2 - 1) - 6(x - 1)
= x(x + 1)(x - 1) - 6(x - 1)
= (x - 1) [x(x + 1) - 6]
= (x - 1) (x2 + x - 6) .
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