\(\left(3x^2-2y\right)^3=27x^6-54x^4y+36x^2y^2-8y^3\)

Lời giải:

a. $=(2x)^2-2.2x.5y+(5y)^2=4x^2-20xy+25y^2$
b. $=(3x)^2+2.3x.2y+(2y)^2=9x^2+12xy+4y^2$

c. $=(4y+3x)(4y-3x)=(4y)^2-(3x)^2=16y^2-9x^2$

\(a.4x^2-10xy+25y^2\)

\(b.9x^2+6xy+4y^2\)

\(c.16y^2-9x^2\)

Giải:

a) \(\left(3x^2-2y^3\right)^2\)

\(=\left(3x^2\right)^2-2.3x.2y+\left(2y^3\right)^2\)

\(=9x^4-12xy+4y^6\)

Vậy ...

b) \(\left(-2x^2-3\right)^2\)

\(=\left(-2x^2\right)^2-2.2x^2.3+3^2\)

\(=4x^4-12x^2+9\)

Vậy ...

a) \(\left(3x^2-2y^3\right)^2\)

\(=\left(3x^2\right)^2-2\cdot3x^2\cdot2y^3+\left(2y^3\right)^2\)

\(=9x^4-12x^2y^3+4y^6\)

b) \(\left(-2x^2-3\right)^2\)

\(=\left(-2x^2\right)^2-2\cdot\left(-2x^2\right)\cdot3+3^2\)

\(=4x^4+12x^2+9\)

a,\(\left(x^2+2xy\right)^3=\left(x^2\right)^3+3.\left(x^2\right)^2.2xy+3.\left(2xy\right)^2.x^2+\left(2xy\right)^3\)

\(=x^6+6x^5y+12x^4y^2+8x^3y^3\)

b,\(\left(3x^2-2y\right)^3=\left(3x^2\right)^3-3.\left(3x^2\right)^2.2y+3.\left(2y\right)^2.3x^2-\left(2y\right)^3\)

\(=27x^6-54x^4y+36y^2x^2-8y^3\)

c,\(\left(2x^3-y^2\right)^3=8x^9-12x^6y^2+6x^3y^4-y^6\)

a) \({\left( {x - 2} \right)^4}\)

\(\begin{array}{l} = {x^4} + 4{x^3}.\left( { - 2} \right) + 6{x^2}.{\left( { - 2} \right)^2} + 4x{\left( { - 2} \right)^3} + {\left( { - 2} \right)^4}\\ = {x^4} - 8{x^3} + 24{x^2} - 32x + 16\end{array}\)

b) \({\left( {x + 2y} \right)^5}\)

\(\begin{array}{l} = {x^5} + 5.{x^4}.\left( {2y} \right) + 10.{x^3}.{\left( {2y} \right)^2} + 10.{x^2}.{\left( {2y} \right)^3} + 5.x.{\left( {2y} \right)^4} + 1.{\left( {2y} \right)^5}\\ = {x^5} + 10{x^4}y + 40{x^3}{y^3} + 80{x^2}{y^3} + 80x{y^4} + 32{y^5}\end{array}\)

a) \(\left(x^2+2xy\right)^3\)

\(=\left(x^2\right)^3+3\left(x^2\right)^22xy+3x^2\left(2xy\right)^2+\left(2xy\right)^3\)

\(=x^6+6x^5y+12x^4y^2+8x^3y^3\)

b) \(\left(3x^2-2y\right)^3\)

\(=\left(3x^2\right)^3-3\left(3x^2\right)^22y+3.3x^2\left(2y\right)^2-\left(2y\right)^3\)

\(=27x^6-54x^4y+36x^2y^2-8y^3\)

c) \(\left(2x^3-y^2\right)^3\)

\(=\left(2x^3\right)^3-3\left(2x^3\right)^2y^2+3.2x^3\left(y^2\right)^2-\left(y^2\right)^3\)

\(=8x^9-12x^6y^2+6x^3y^4-y^6.\)

Câu 1: \(3x+2\left(5-x\right)=0\)

\(\Rightarrow3x+10-2x=0\)

\(\Rightarrow x+10=0\)

\(\Rightarrow x=-10\).

Câu 2: \(2x\left(5-3x\right)+2x\left(3x-5\right)-3\left(x-7\right)=3\)

\(\Rightarrow2x\left(5-3x\right)-2x\left(5-3x\right)-3\left(x-7\right)=0\)

\(\Rightarrow\left(2x-2x\right)\left(5-3x\right)-3\left(x-7\right)=3\)

\(\Rightarrow-3\left(x-7\right)=3\)

\(\Rightarrow x-7=-1\)

\(\Rightarrow x=6.\)

Câu 3:

Áp dụng hằng đẳng thức mở rộng có:

\(\left(a+b+c\right)\left(a^2+b^2+c^2-ab-bc-ca\right)\)

\(=a^3+b^3+c^3-3abc.\)

Câu 4: \(3x^2\left(3x^2-2y^2\right)-\left(3x^2-2y^2\right)\left(3x^2+2y^2\right)\)

\(=\left(3x^2-2y^2\right)\left[3x^2-\left(3x^2+2y^2\right)\right]\)

\(=\left(3x^2-2y^2\right)\left(-2y^2\right)\)

\(=-6x^2y^2+4y^3.\)

Câu 5:

Ta có: \(R=\left(2x-3\right)\left(4+6x\right)-\left(6-3x\right)\left(4x-2\right)\)

\(=\left(8x-12+12x^2-18x\right)-\left(24x-12x^2-12+6x\right)\)

\(=12x^2-10x-12-24x+12x^2+12-6x\)

\(=24x^2-40x.\)

Câu1:

\(3x+2\left(5-x\right)=0\)

\(\Leftrightarrow3x+10-2x=0\)

\(\Leftrightarrow x=-10\)

Câu 2:

\(2x\left(5-3x\right)+2x\left(3x-5\right)-3\left(x-7\right)=3\)

\(\Leftrightarrow2x\left(5-3x+3x-5\right)-3x-21=3\)

\(\Leftrightarrow-3x=24\)

\(\Rightarrow x=-8\)

câu 3:

\(\left(a+b+c\right)\left(a^2+b^2+c^2-ab-bc-ca\right)\)

\(=\left(a+b+c\right)\left(a^2+2ab+b^2-ac-bc+c^2-3ab\right)\)

\(=\left(a+b+c\right)\left(a^2+2ab+b^2-ac-bc+c^2\right)-3ab\left(a+b+c\right)\)

\(=\left(a+b+c\right)\left[\left(a+b\right)^2-c\left(a+b\right)+c^2\right]-3a^2b-3ab^2-3abc\)\(=\left(a+b\right)^3+c^3-3a^2b-3ab^2-3abc\)

\(=a^3+3a^2b+3ab^2+b^3+c^3-3a^2b-3ab^2-3abc\)\(=a^3+b^2+c^3-3abc\)

Câu 4:

\(3x^2\left(3x^2-2y^2\right)-\left(3x^2-2y^2\right)\left(3x^2+2y^2\right)\)

\(=\left(3x^2-2y^2\right)\left(3x^2-3x^2-2y^2\right)\)

\(=-2y^2\left(3x^2-2y^2\right)\)

Câu 5:

\(\left(2x-3\right)\left(4+6x\right)-\left(6-3x\right)\left(4x-2\right)\)

\(=\left(2x-3\right)2\left(2+3x\right)-3\left(2-x\right)2\left(2x-1\right)\)

\(=2\left(4x^2-9\right)-6\left(3x-2-2x^2\right)\)

\(=8x^2-18-18x+12+12x^2\)

\(=20x^2-18x-6\)

a. (2x+3y)²= (2x)²+2.2x.3y+(3y)²

=4x²+12xy+9y²

b. 2(\(\dfrac{1}{2}\)x²+y)(x²-2y)

=(x²+2y)(x²-2y)

=x⁴-4y²

c, (x+y+z)²= [(x+y)+z]²

=(x+y)²+2(x+y)z+z²

=x²+2xy+y²+2xz+2yz+z²

=x²+y²+z²+2xy+2yz+2xz