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b) 6x - 9 - x2
= - (x2 - 6x + 9 )
= - ( x2 - 2.x.3 + 32 )
= - ( x - 3 )2
c) x2 - 16
= x2 - 42
= ( x - 4 )( x + 4)
d) 9x2 - 25
= ( 3x )2 - 52
= ( 3x - 5 )( 3x + 5 )
e ) x4 - y4
= ( x2)2 - ( y2 )2
= ( x2 - y2 )( x2 + y2 )
f) x6 -y6
= ( x3 )2 - ( y3)2
=( x3 - y3 )( x3 + y3 )
g) 8x3 - \(\dfrac{1}{27}\)
= ( 2x )3 - ( \(\dfrac{1}{3}\))3
= ( 2x - \(\dfrac{1}{3}\) ) ( 2x + \(\dfrac{2}{3}\)x + \(\dfrac{1}{3}\))
Bài giải:
1.
a) x2 + 6x + 9 = x2 + 2 . x . 3 + 32 = (x + 3)2
b) 10x – 25 – x2 = -(-10x + 25 +x2) = -(25 – 10x + x2)
= -(52 – 2 . 5 . x – x2) = -(5 – x)2
c) 8x3 - 1818 = (2x)3 – (1212)3 = (2x - 1212)[(2x)2 + 2x . 1212 + (1212)2]
= (2x - 1212)(4x2 + x + 1414)
d) 125125x2 – 64y2 = (15x)2(15x)2- (8y)2 = (1515x + 8y)(1515x - 8y)
2.
a) x3 + 127127 = x3 + (1313)3 = (x + 1313)(x2 – x . 1313+ (1313)2)
=(x + 1313)(x2 – 1313x + 1919)
b) (a + b)3 – (a - b)3
= [(a + b) – (a – b)][(a + b)2 + (a + b) . (a – b) + (a – b)2]
= (a + b – a + b)(a2 + 2ab + b2 + a2 – b2 + a2 – 2ab + b2)
= 2b . (3a3 + b2)
c) (a + b)3 + (a – b)3 = [(a + b) + (a – b)][(a + b)2 – (a + b)(a – b) + (a – b)2]
= (a + b + a – b)(a2 + 2ab + b2 – a2 +b2 + a2 – 2ab + b2]
= 2a . (a2 + 3b2)
d) 8x3 + 12x2y + 6xy2 + y3 = (2x)3 + 3 . (2x)2 . y +3 . 2x . y + y3 = (2x + y)3
e) - x3 + 9x2 – 27x + 27 = 27 – 27x + 9x2 – x3 = 33 – 3 . 32 . x + 3 . 3 . x2 – x3 = (3 – x)3
\(16-x^2=4^2-x^2=\left(4-x\right)\left(4+x\right)\)
\(4x^2-9=\left(2x\right)^2-3^2=\left(2x-3\right)\left(2x+3\right)\)
\(a^4-25=\left(a^2\right)^2-5^2=\left(a^2-5\right)\left(a^2+5\right)\)
\(\left(a+b\right)^2-1=\left(a+b\right)^2-1^2=\left(a+b-1\right)\left(a+b+1\right)\)
\(\left(a+b\right)^2-\left(m-n\right)^2=\left(a+b-m+n\right)\left(a+b+m-n\right)\)
\(x^3-27=x^3-3^3=\left(x-3\right)\left(x^2+3x+9\right)\)
\(64x^3+\dfrac{1}{27}=\left(4x\right)^3+\left(\dfrac{1}{3}\right)^3=\left(4x+\dfrac{1}{3}\right)\left(16x^2-\dfrac{4}{3}x+\dfrac{1}{9}\right)\)
\(\left(m-n\right)^6-6\left(m-n\right)^4+12\left(m-n\right)^2-8=\left[\left(m-n\right)^2-2\right]^3\)
\(\dfrac{8}{27}a^3-\dfrac{8}{3}a^2b+8b^2a-8b^3=\left(\dfrac{2}{3}a-2b\right)^3\)
Chúc bạn học tốt !!
Bài làm
a) 812 : 46 = 236 : 212 = 214
b) 276 : 92 = 318 : 34 = 314
còn tiếp....
Bài làm
c) \(\frac{9^{15}.25^3.4^3}{3^{10}.50^6}\)
\(=\frac{3^{30}.5^6.2^6}{3^{10}.2^6.5^{12}}\)
\(=\frac{3^{20}.1.1}{1.1.5^6}\)
\(=\frac{\text{3486784401}}{\text{15625}}\)
16.(-61)+27=3.(4^n+9)-1024
<=>-949=3.(4^n+9)-1024
<=>75=3.(4^n+9)
<=>4^n+9=25
<=>4^n=16
<=>n=2
Vậy n=2
\(16-x^2=4^2-x^2=\left(4-x\right)\left(4+x\right)\)
\(4x^2-9=\left(2x\right)^2-3^2=\left(2x-3\right)\left(2x+3\right)\)
\(a^4-25=\left(a^2\right)^2-5^2=\left(a^2-5\right)\left(a^2+5\right)\)
\(\left(a+b\right)^2-1=\left(a+b\right)^2-1^2=\left(a+b-1\right)\left(a+b-1\right)\)
\(\left(a+b\right)^2-\left(m-n\right)^2=\left(a+b-m+n\right)\left(a+b+m-n\right)\)
\(x^3-27=x^3-3^3=\left(x-3\right)\left(x^2+3x+3^2\right)\)
\(64x^3+\frac{1}{27}=\left(4x\right)^3+\left(\frac{1}{3}\right)^3=\left(4x+\frac{1}{3}\right)\left(16x^2+\frac{4}{3}x+\frac{1}{9}\right)\)
Tham khảo~
\(16-x^2=4^2-x^2=\left(4-x\right)\left(4+x\right)\)
\(4x^2-9=\left(2x\right)^2-3^2=\left(2x+3\right)\left(2x-3\right)\)
\(a^4-25=\left(a^2\right)^2-5^2=\left(a^2+5\right)\left(a^2-5\right)\)
\(\left(a+b\right)^2-1=\left(a+b+1\right)\left(a+b-1\right)\)
\(\left(a+b\right)^2-\left(m-n\right)^2=\left(a+b+m-n\right)\left(a+b-m+n\right)\)
\(x^3-27=x^3-3^3=\left(x-3\right)\left(x^2+3x+9\right)\)
\(64x^3+\frac{1}{27}=\left(4x\right)^3+\left(\frac{1}{3}\right)^3=\left(4x+\frac{1}{3}\right)\left(16x^2-\frac{4}{3}x+\frac{1}{9}\right)\)
a) \(3\left(5-4n\right)+\left(27+2n\right)>0\)
\(\Leftrightarrow15-12n+27+2n>0\)
\(\Leftrightarrow42-10n>0\)
\(\Leftrightarrow-10n>-42\Leftrightarrow n< 4,2\)
Vậy \(S=\left\{n|n< 4,2\right\}\)
b) \(\left(n+2\right)^2-\left(n-3\right)\left(n+3\right)\le40\)
\(\Leftrightarrow n^2+4n+4-n^2+9\le40\)
\(\Leftrightarrow4n+13\le40\)
\(\Leftrightarrow4n\le27\Leftrightarrow n\le6,75\)
Vậy \(S=\left\{n|n\le6,75\right\}\)
a/ \(\dfrac{2^n}{32}=4\)
\(\Leftrightarrow\dfrac{2^n}{2^5}=2^2\)
\(\Leftrightarrow2^n=2^7\)
\(\Leftrightarrow n=7\)
Vậy ...
b/ \(27^n.9^n=9^{27}:81\)
\(\Leftrightarrow3^{3n}.3^{2n}=3^{54}:3^4\)
\(\Leftrightarrow3^{2n+3n}=3^{50}\)
\(\Leftrightarrow2n+3n=50\)
\(\Leftrightarrow5n=50\)
\(\Leftrightarrow n=10\)
Vậy ...