BÀi 1:

a: \(\left(a+b\right)^2-\left(a-b\right)^2\)

=(a+b-a+b)(a+b+a-b)

\(=2b\cdot2a=4ab\)

b: \(\left(a+2\right)^2-\left(a+2\right)\left(a-2\right)\)

\(=a^2+4a+4-\left(a^2-4\right)\)

\(=a^2+4a+4-a^2+4=4a+8\)

c: \(\left(2x+3\right)^2-4\left(x-1\right)\left(x+1\right)=49\)

=>\(4x^2+12x+9-4\left(x^2-1\right)=49\)

=>\(4x^2+12x+9-4x^2+4=49\)

=>12x+13=49

=>12x=36

=>x=3

d: \(Q=\left(x+3\right)^2+\left(x+3\right)\left(x-3\right)-2\left(x+2\right)\left(x-4\right)\)

\(=x^2+6x+9+x^2-9-2\left(x^2-4x+2x-8\right)\)

\(=2x^2+6x-2\left(x^2-2x-8\right)=2x^2+6x-2x^2+4x+16=10x+16\)

Khi x=1/2 thì Q=10*1/2+16=5+16=21

Bài 2:

a: \(A=\left(4x^2+y^2\right)\left(2x+y\right)\left(2x-y\right)\)

\(=\left(4x^2+y^2\right)\left(4x^2-y^2\right)=16x^4-y^4\)

b: \(\left(7x+1\right)^2-\left(x+7\right)^2\)

\(=49x^2+14x+1-\left(x^2+14x+49\right)\)

\(=49x^2+14x+1-x^2-14x-49=48x^2-48=48\left(x^2-1\right)\)

c: \(16x^2-\left(4x-5\right)^2=15\)

=>\(16x^2-\left(16x^2-40x+25\right)=15\)

=>\(16x^2-16x^2+40x-25=15\)

=>40x=40

=>x=1

d: \(A=-x^2+2x+3\)

\(=-x^2+2x-1+4\)

\(=-\left(x-1\right)^2+4\le4\forall x\)

Dấu '=' xảy ra khi x-1=0

=>x=1

a)x²-6x+9

=x²-2.x.3+3²

=(x-3)²

b)4x²+4x+1

=(2x)²+2.2x.1+1²

=(2x+1)²

c)4x²+12xy+9y²

=(2x)²+2.2x.3y+(3y)²

=(2x+3y)²

d)4x⁴-4x²+4

=(2x²)²-2.2x².2+2²

=(2x²-2)²

a. Rút gọn và sắp xếp

P(x) = -5x3 - 2x + 4x4 + 3 + 3x2 - 4x4 + 10x3 - 8

= 5x3 + 3x2-2x-5 (0.75 điểm)

Q(x) = 6x2 + 5x3 - 3x5 + 4 + 8x - 4x2 + 3x5 - 10x

= 5x3 + 2x2 - 2x + 4 (0.75 điểm)

i) x³- 11x² + 30x

=\(x\left(x^2-11x+30\right)\)

=\(x\left(x-6\right)\left(x-5\right)\)

j) 4x⁴- 21x²y² + y⁴

=4x^4+4x^2y^2+y^4-25x^2y^2

=(2x^2+y^2)^2-(5xy)^2

=(2x^2+y^2-5xy)(2x^2+y^2+5xy)

1.
A= \(2\sqrt{6}\) + \(6\sqrt{6}\) - \(8\sqrt{6}\)
A= 0
2.
A= \(12\sqrt{3}\) + \(5\sqrt{3}\) - \(12\sqrt{3}\)
A= 0
3.
A= \(3\sqrt{2}\) - \(10\sqrt{2}\) + \(6\sqrt{2}\)
A= -\(\sqrt{2}\)
4.
A= \(3\sqrt{2}\) + \(4\sqrt{2}\) - \(\sqrt{2}\)
A= \(6\sqrt{2}\)
5.
M= \(2\sqrt{5}\) - \(3\sqrt{5}\) + \(\sqrt{5}\)
M= 0
6.
A= 5 - \(3\sqrt{5}\) + \(3\sqrt{5}\)
A= 5

This literally took me a while, pls sub :D
https://www.youtube.com/channel/UC4U1nfBvbS9y_Uu0UjsAyqA/featured

\(A=2x^2+2xy+x^2-2xy+y^2-4y^2=3x^2-3y^2\)

\(A=2x^2+2xy+x^2-2xy+y^2-4y^2=3x^2-3y^2\)

\(a,\)

với \(a=100\)

\(=>9x^2+30x+25=\left(3x\right)^2+2.3.5x+5^2=\left(3x_{ }+5\right)^2\)

\(b,\)

với \(a=\dfrac{1}{25}\)

\(25x^2-2x+\dfrac{1}{25}=\left(5x\right)^2-2.5.x.\dfrac{1}{5}+\left(\dfrac{1}{5}\right)^2=\left(5x-\dfrac{1}{5}\right)^2\)

\(c,\)

với  \(a=6\)

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

\(d.\)

với \(a=\dfrac{4}{3}\)

\(=>\left(2x\right)^2-2.2.\dfrac{1}{3}x+\left(\dfrac{1}{3}\right)^2=\left(2x-\dfrac{1}{3}\right)^2\)

4x⁴ - 4x² + 1

Gọi x² là t, ta có:

4t² - 4t + 1

= (2t)² - 2.2t.1 + 1²

= (2t - 1)²

= (2x² - 1)²

=(2x²)²-2.2x².1+1=(2x²-1)²

\(=8x^3+27-8x^3-7=20\)

bằng 20