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a) M = (x² + 3xy - 3x³) + (2y³ - xy + 3x³)
= x² + 3xy - 3x³ + 2y³ - xy + 3x³
= x² + (3xy - xy) + (-3x³ + 3x³) + 2y³
= x² + 2xy + 2y³
Tại x = 5 và y = 4
M = 5² + 2.5.4 + 2.4³
= 25 + 40 + 2.64
= 65 + 128
= 193
b) N = x²(x + y) - y(x² - y²)
= x³ + x²y - x²y + y³
= x³ + (x²y - x²y) + y³
= x³ + y³
Tại x = -6 và y = 8
N = (-6)³ + 8³
= -216 + 512
= 296
c) P = x² + 1/2 x + 1/16
= (x + 1/2)²
Tại x = 3/4 ta có:
P = (3/4 + 1/2)² = (5/4)² = 25/16
Bài 1:
a.\(\left(x+y\right)^2-\left(x-y\right)^2=\left(x+y-x+y\right)\left(x+y+x-y\right)=2\left(x+y\right)\)
b.\(2\left(x+y\right)\left(x-y\right)+\left(x+y\right)^2+\left(x-y\right)^2=\left(x+y+x-y\right)^2=4x^2\)
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a/ \(x\left(x+4\right)\left(x-4\right)-\left(x^2-1\right)\left(x^2+1\right)=x\left(x^2-16\right)-x^4+1=-x^4+x^3-16x+1\)
b/ \(\left(y-3\right)\left(y+3\right)\left(y^2+9\right)-\left(y^2+2\right)\left(y^2-2\right)=\left(y^2-9\right)\left(y^2+9\right)-y^4+4=y^4-81-y^2+4=-77\)
bài 1.
a.\(A=x^2-2xy+y^2+x^2+2xy+y^2=2\left(x^2+y^2\right)\)
b.\(B=x^2+2xy+y^2-\left(x^2-2xy+y^2\right)=4xy\)
c.\(C=4a^2+4ab+b^2-\left(4a^2-4ab+b^2\right)=8ab\)
d.\(D=4x^2-4x+1-2\left(4x^2-12x+9\right)+4=-4x^2+20x-13\)
.bài 2
a.\(A=x^2+6x+9+x^2-9-2\left(x^2-2x-8\right)=10x+16;x=-\frac{1}{2}\Rightarrow A=9\)
b.\(B=9x^2+24x+16-x^2+16-10x=8x^2+14x+32\Rightarrow x=-\frac{1}{10}\Rightarrow B=\frac{767}{25}\)
c.\(C=x^2+2x+1-\left(4x^2-4x+1\right)+3\left(x^2-4\right)=6x-12\Rightarrow x=1\Rightarrow C=-6\)
d.\(D=x^2-9+x^2-4x+4-2x^2+8x=4x-5\Rightarrow x=-1\Rightarrow A=-9\)
Trả lời:
Bài 1: Rút gọn biểu thức:
a) A = ( x - y )2 + ( x + y )2
= x2 - 2xy + y2 + x2 + 2xy + y2
= 2x2 + 2y2
b) B = ( x + y )2 - ( x - y )2
= x2 + 2xy + y2 - ( x2 - 2xy + y2 )
= x2 + 2xy + y2 - x2 + 2xy - y2
= 4xy
c) C = ( 2a + b )2 - ( 2a - b )2
= 4a2 + 4ab + b2 - ( 4a2 - 4ab + b2 )
= 4a2 + 4ab + b2 - 4a2 + 4ab - b2
= 8ab
d) D = ( 2x - 1 )2 - 2 ( 2x - 3 )2 + 4
= 4x2 - 4x + 1 - 2 ( 4x2 - 12x + 9 ) + 4
= 4x2 - 4x + 1 - 8x2 + 24x - 18 + 4
= - 4x2 + 20x - 13
Bài 2: Rút gọn rồi tính giá trị biểu thức:
a) A = ( x + 3 )2 + ( x - 3 )( x + 3 ) - 2 ( x + 2 )( x - 4 )
= x2 + 6x + 9 + x2 - 9 - 2 ( x2 - 2x - 8 )
= 2x2 + 6x - 2x2 + 4x + 16
= 10x + 16
Thay x = 1/2 vào A, ta có:
\(A=10.\left(-\frac{1}{2}\right)+16=-5+16=11\)
b) B = ( 3x + 4 )2 - ( x - 4 )( x + 4 ) - 10x
= 9x2 + 24x + 16 - x2 + 16 - 10x
= 8x2 + 14x + 32
Thay x = - 1/10 vào B, ta có:
\(B=8.\left(-\frac{1}{10}\right)^2+14.\left(-\frac{1}{10}\right)+32=\frac{767}{25}\)
c) C = ( x + 1 )2 - ( 2x - 1 )2 + 3 ( x - 2 )( x + 2 )
= x2 + 2x + 1 - 4x2 + 4x - 1 + 3 ( x2 - 4 )
= - 3x2 + 6x + 3x2 - 12
= 6x - 12
Thay x = 1 vào C, ta có:
\(C=6.1-12=-6\)
d) D = ( x - 3 )( x + 3 ) + ( x - 2 )2 - 2x ( x - 4 )
= x2 - 9 + x2 - 4x + 4 - 2x2 + 8x
= 4x - 5
Thay x = - 1 vào D, ta có:
\(D=4.\left(-1\right)-5=-9\)
a: \(P=\left(5x-1-5x-4\right)^2=\left(-3\right)^2=9\)
b: \(Q=\left(x+y\right)^3-3xy\left(x+y\right)=x^3+y^3\)
c: \(=\dfrac{\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)}{2}\)
\(=\dfrac{\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)}{2}\)
\(=\dfrac{\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)}{2}\)
\(=\dfrac{5^{32}-1}{2}\)
\(1,\left(x+y\right)^2-\left(x-y\right)^2=\left[\left(x+y\right)-\left(x-y\right)\right]\left[\left(x+y\right)+\left(x-y\right)\right]=\left(x+y-x+y\right)\left(x+y+x-y\right)=2y.2x=4xy\)
\(2,\left(x+y\right)^3-\left(x-y\right)^3-2y^3\)
\(=x^3+3x^2y+3xy^2+y^3-x^3+3x^2y-3xy^2+y^3-2y^3\)
\(=6x^2y\)
\(3,\left(x+y\right)^2-2\left(x+y\right)\left(x-y\right)+\left(x-y\right)^2\\ =\left[\left(x+y\right)-\left(x-y\right)\right]^2\\ =\left(x+y-x+y\right)^2\\ =4y^2\)
\(4,\left(2x+3\right)^2-2\left(2x+3\right)\left(2x+5\right)+\left(2x+5\right)^2\\ =\left[\left(2x+3\right)-\left(2x+5\right)\right]^2\\ =\left(2x+3-2x-5\right)^2\\ =\left(-2\right)^2\\ =4\)
\(5,9^8.2^8-\left(18^4+1\right)\left(18^4-1\right)\\ =18^8-\left[\left(18^4\right)^2-1\right]\\ =18^8-18^8+1\\ =1\)
1: =x^2+2xy+y^2-x^2+2xy-y^2=4xy
2: =x^3+3x^2y+3xy^2+y^3-x^3+3x^2y-3xy^2+y^3-2y^3
=6x^2y
3: =(x+y-x+y)^2=(2y)^2=4y^2
4: =(2x+3-2x-5)^2=(-2)^2=4
5: =18^8-18^8+1=1
