a: \(\left(x+2\right)^2=x^2+2\cdot x\cdot2+2^2=x^2+4x+4\)

b: \(\left(2x+y\right)^2=\left(2x\right)^2+2\cdot2x\cdot y+y^2=4x^2+4xy+y^2\)

c: \(\left(x-3y\right)^2=x^2-2\cdot x\cdot3y+\left(3y\right)^2=x^2-6xy+9y^2\)

d: \(\left(\dfrac{1}{2}x-y\right)^2=\left(\dfrac{1}{2}x\right)^2-2\cdot\dfrac{1}{2}x\cdot y+y^2\)

\(=\dfrac{1}{4}x^2-xy+y^2\)

e: \(\left(x^2-y\right)^2=\left(x^2\right)^2-2\cdot x^2y+y^2=x^4-2x^2y+y^2\)

a) \(\left(x+2\right)^2\)

\(=x^2+2\cdot x\cdot2+2^2\)

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

b) \(\left(2x+y\right)^2\)

\(=\left(2x\right)^2+2\cdot2x\cdot y+y^2\)

\(=4x^2+4xy+y^2\)

c) \(\left(x-3y\right)^2\)

\(=x^2-2\cdot x\cdot3y+\left(3y\right)^2\)

\(=x^2-6xy+9y^2\)

d) \(\left(\dfrac{1}{2}x-y\right)^2\)

\(=\left(\dfrac{1}{2}x\right)^2-2\cdot\dfrac{1}{2}x\cdot y+y^2\)

\(=\dfrac{x^2}{4}-xy+y^2\)

e) \(\left(x^2-y\right)^2\)

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

\(=x^4-2x^2y+y^2\)

a)(x+2)²=x²+2×x×2+2²=x²+4x+2

b)(2x+y)²=(2x)²+2×2x×y+y²=4x²+4xy+y²

c)(x-3y)²=x²-2×x×3y+(3y)²=x²-6xy+9y

d)(1/2x-y)²=(1/2x)²-2×1/2x×y+y²=1/4x²-xy+y²

e)(x²-y)²=(x²)²-2×x²×y+y²=x⁴-2x²y+y²

Câu 1: D

Câu 2: D

a: \(\left(2x-3\right)^2=4x^2-12x+9\)

b: \(\left(x-3y\right)^2=x^2-6xy+9y^2\)

c: \(=4x^2-9y^2-4x^2-4xy-y^2\)

\(=-10y^2-4xy\)

d: \(\left(x+3y^2\right)^2=x^2+6xy^2+9y^4\)

a: \(\left(2x-3\right)^2=4x^2-12x+9\)

b: \(\left(x-3y\right)^2=x^2-6xy+9y^2\)

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

\(=4x^2-9y^2-4x^2-4xy-y^2=-8y^2-4xy\)

d: \(\left(x+3y^2\right)^2=x^2+6xy^2+9y^4\)

Chỉ cần dựa vào 7 hằng đẳng thức thôi nha bạn:

\(\left(2x-3\right)^2=2x^2-12x+9\)

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

\(\left(2x+3y\right)\left(2x-3y\right)-\left(2x+y\right)^2=2x^2-3y^2-2x^2+4xy-y^2=-3y^2+4xy-y^2\)\(\left(x+3y^2\right)^2=x^2+3y^22x+3y^4\)

Bạn dùng hằng đẳng thức ý

a. (A – B)²= A² – 2AB+ B²

^b. (A – B)²= A² – 2AB+ B²

c. (2x+3y)(2x-3y)-(2x+y)²

= 4x²-9y² -4x² - 4xy-y²

= -10y²-4x²

d. (A+B)² = A²+2AB+B²

giúp mình với ah đang cần gấp ah

C

\(A=4x^2+12x+9\\ B=121x^2-44x+4\\ C=16x^2-9y^2\\ D=4x^2+20x+25\\ E=x^2-12x+36\)

a) (2x)^2 +12x+9

b)(11x)^2 -44x +4

c)48x^2y -36xy^2

d)4x^2 +20x +25

e)x^2 -12x +36

a) \(A=\left(2x+3\right)^2=4x^2+12x+9\)

b) \(B=\left(11x-2\right)^2=121x^2-44x+4\)

c) \(C=\left(4x+3y\right)\left(4x-3y\right)=16x^2-9y^2\)

d) \(D=\left(2x+5\right)^3=8x^3+60x^2+150x+125\)

e) \(E=\left(x-6\right)^3=x^3-18x^2+108x+216\)

a) \(x^4-y^4\)

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

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

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

b) \(x^2-3y^2\)

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

\(=\left(x-y\sqrt{3}\right)\left(x+y\sqrt{3}\right)\)

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

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

\(=\left(5x-5y\right)\left(x+y\right)\)

\(=5\left(x-y\right)\left(x+y\right)\)

d) \(9\left(x-y\right)^2-4\left(x+y\right)^2\)

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

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

\(=\left(5x-y\right)\left(x-5y\right)\)

e) \(\left(4x^2-4x+1\right)-\left(x+1\right)^2\)

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

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

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

f) \(x^3+27\)

\(=x^3+3^3\)

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

g) \(27x^3-0,001\)

\(=\left(3x\right)^3-\left(0,1\right)^3\)

\(=\left(3x-0,1\right)\left(9x^2+0,3x+0,01\right)\)

h) \(125x^3-1\)

\(=\left(5x\right)^3-1^3\)

\(=\left(5x-1\right)\left(25x^2+5x+1\right)\)