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9) \(\left(a+b\right)^3-\left(a-b\right)^3\)
\(=\left(a+b-a+b\right)\left[\left(a+b\right)^2+\left(a+b\right)\left(a-b\right)+\left(a-b\right)^2\right]\)
\(=b^2\left[a^2+2ab+b^2+a\left(a-b\right)+b\left(a-b\right)+a^2-2ab+b^2\right]\)
\(=b^2\left(a^2+2ab+b^2+a^2-ab+ab-b^2+a^2-2ab+b^2\right)\)
\(=b^2\left(3a^2+b^2\right)\)
10) \(\left(6x-1\right)^2-\left(3x+2\right)^2\)
\(=\left(6x-1-3x-2\right)\left(6x-1+3x+2\right)\)
\(=\left(3x-3\right)\left(9x+1\right)\)
11) \(x^2-4x^2y^2+y^2+2xy\)
\(=\left(x^2+2xy+y^2\right)-4x^2y^2\)
\(=\left(x+y\right)^2-\left(2xy\right)^2\)
\(=\left(x+y-2xy\right)\left(x+y+2xy\right)\)
12) \(\left(x^2-25\right)^2-\left(x-5\right)^2\)
\(=\left(x^2-25-x+5\right)\left(x^2-25+x-5\right)\)
\(=\left(x^2-x-20\right)\left(x^2-30+x\right)\)
13) \(x^6-x^4+2x^3+2x^2\)
\(=x^6-x^4+2x^3+2x^2-1+1\)
\(=\left(x^6+2x^3+1\right)-\left(x^4-2x^2+1\right)\)
\(=\left[\left(x^3\right)^2+2x^3.1+1^2\right]-\left[\left(x^2\right)^2-2x^2.1+1^2\right]\)
\(=\left(x^3+1\right)^2-\left(x^2-1\right)^2\)
\(=\left(x^3+1-x^2+1\right)\left(x^3+1+x^2-1\right)\)
\(=\left(x^3-x^2+2\right)\left(x^3+x^2\right)\)
1) \(\left(x+y\right)^2-25\)
\(=\left(x+y\right)^2-5^2\)
\(=\left(x+y-5\right)\left(x+y+5\right)\)
2) \(100-\left(3x-y\right)^2\)
\(=10^2-\left(3x-y\right)^2\)
\(=\left(10-3x+y\right)\left(10+3x-y\right)\)
3) \(64x^2-\left(8a+b\right)^2\)
\(=\left(8x\right)^2-\left(8a+b\right)^2\)
\(=\left(8x-8a-b\right)\left(8x+8a+b\right)\)
4) \(4a^2b^4-c^4d^2\)
\(=\left(2ab^2\right)^2-\left(c^2d\right)^2\)
\(=\left(2ab^2-c^2d\right)\left(2ab^2+c^2d\right)\)
5) Đề đúng ko vậy ạ?
6) \(16x^3+54y^3\)
\(=2\left(8x^3+27y^3\right)\)
\(=2\left[\left(2x\right)^3+\left(3y\right)^3\right]\)
\(=2\left(2x+3y\right)\left[\left(2x\right)^2-2x.3y+\left(3y\right)^2\right]\)
\(=2\left(2x+3y\right)\left(4x^2-6xy+9y^2\right)\)
7) \(8x^3-y^3\)
\(=\left(2x\right)^3-y^3\)
\(=\left(2x-y\right)\left[\left(2x\right)^2+2xy+y^2\right]\)
\(=\left(2x-y\right)\left(4x^2+2xy+y^2\right)\)
8) \(\left(a+b\right)^2-\left(2ab-b\right)^2\)
\(=\left(a+b-2ab+b\right)\left(a+b+2ab-b\right)\)
\(=\left(a+2b-2ab\right)\left(a+2ab\right)\)
Ta có : 6x2 - 11x + 3
= 6x2 - 2x - 9x + 3
= (6x2 - 2x) - (9x - 3)
= 2x(3x - 1) - 3(3x - 1)
= (2x - 3)(3x - 1)
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) .
CÁC Ý SAU TƯƠNG TỰ
1
x3-7x+6
=x3+0x2-7x +6
= x3-x2+x2-x-6x+6
=(x3-x2)+(x2-x)-(6x-6)
=x2(x-1)+x(x-1)-6(x-1)
=(x-1)(x2+x-6)
=(x-1)(x2+3x-2x-6)
=(x-1)[x(x+3)-2(x+3)]
=(x-1)(x-2)(x+3)
7) (x+2)(x+3)(x+4)(x+5)-24
=(x+2)(x+5) (x+3)(x+4)-24
=[x(x+5)+2(x+5)][x(x+4)+3(x+4)]-24
=[x2+5x+2x+10][x2+4x+3x+12]-24
=[x2+7x+10][x2+7x+12]-24
đặt a=x2+7x+10
=>x2+7x+12=a+2
=a(a+2)-24
=a2+2a-24
=a2+6a-4a-24
=(a2+6a)-(4a+24)
=a(a+6)-4(a+6)
=(a+6)(a-4)
thay a= x2+7x+10 vào ta được
(x2+7x+10+6)(x2+7x+10-4)
=(x2+7x+16)(x2+7x+6)
1: \(\left(2x+1\right)^3=\left(2x\right)^3+3\cdot\left(2x\right)^2\cdot1+3\cdot2x\cdot1^2+1^3\)
\(=8x^3+12x^2+6x+1\)
2: \(\left(x-\dfrac{2}{3}\right)^3=x^3-3\cdot x^2\cdot\dfrac{2}{3}+3\cdot x\cdot\left(\dfrac{2}{3}\right)^2-\left(\dfrac{2}{3}\right)^3\)
\(=x^3-2x^2+\dfrac{4}{3}x-\dfrac{8}{27}\)
3: \(\left(3x-1\right)^3=\left(3x\right)^3-3\cdot\left(3x\right)^2\cdot1+3\cdot3x\cdot1^2-1^3\)
\(=27x^3-27x^2+9x-1\)
5: \(\left(2-3y\right)^3=2^3-3\cdot2^2\cdot3y+3\cdot2\cdot\left(3y\right)^2-\left(3y\right)^3\)
\(=8-36y+54y^2-27y^3\)
6: \(\left(3x-2y\right)^3=\left(3x\right)^3-3\cdot\left(3x\right)^2\cdot2y+3\cdot3x\cdot\left(2y\right)^2-\left(2y\right)^3\)
\(=27x^3-54x^2y+36xy^2-8y^3\)
7: \(\left(4x+\dfrac{2}{3}y\right)^3=\left(4x\right)^3+3\cdot\left(4x\right)^2\cdot\dfrac{2}{3}y+3\cdot4x\cdot\left(\dfrac{2}{3}y\right)^2+\left(\dfrac{2}{3}y\right)^3\)
\(=64x^3+32x^2y+\dfrac{16}{3}xy^2+\dfrac{8}{27}y^3\)
8: \(\left(x^2-3\right)^3=\left(x^2\right)^3-3\cdot\left(x^2\right)^2\cdot3+3\cdot x^2\cdot3^2-3^3\)
\(=x^6-9x^4+27x^2-27\)
9: \(\left(2x^2-3\right)^3=\left(2x^2\right)^3-3\cdot\left(2x^2\right)^2\cdot3+3\cdot2x^2\cdot3^2-3^3\)
\(=8x^6-36x^4+54x^2-27\)
10: \(\left(\dfrac{1}{2}x+y^2\right)^3\)
\(=\left(\dfrac{1}{2}x\right)^3+3\cdot\left(\dfrac{1}{2}x\right)^2\cdot y^2+3\cdot\dfrac{1}{2}x\cdot\left(y^2\right)^2+\left(y^2\right)^3\)
\(=\dfrac{1}{8}x^3+\dfrac{3}{4}x^2y^2+\dfrac{3}{2}xy^4+y^6\)
11: \(\left(2x-\dfrac{1}{2}y\right)^3=\left(2x\right)^3-3\cdot\left(2x\right)^2\cdot\dfrac{1}{2}y+3\cdot2x\cdot\left(\dfrac{1}{2}y\right)^2-\left(\dfrac{1}{2}y\right)^3\)
\(=8x^3-6x^2y+\dfrac{3}{2}xy^2-\dfrac{1}{8}y^3\)
12: \(\left(x-y^2\right)^2=x^2-2\cdot x\cdot y^2+\left(y^2\right)^2=x^2-2xy^2+y^4\)