Ai đúng và nhanh 3 tick ( part 2 )
Bài 3 : Rút gọn biểu thức :
a) \(A=\left(x-y\right)^2+\left(x+y\right)^2\) b) \(B=\left(2a+b\right)^2-\left(2a-b\right)^2\)
c) \(C=\left(x+y\right)^2-\left(x-y\right)^2\) d) \(D=\left(2x-1\right)^2-2\left(2x-3\right)^2+4\)
Bài 4 : Rút gọn rồi tính giá trị biểu thức :
a) \(A=\left(x+3\right)^2+\left(x-3\right)\left(x+3\right)-2\left(x+2\right)\left(x-4\right)\) Với \(x=-\frac{1}{2}\)
b) \(\left(3x+4\right)^2-\left(x-4\right)\left(x+4\right)-10x\) với \(x=-\frac{1}{10}\)
c) \(C=\left(x+1\right)^2-\left(2x-1\right)^2+3\left(x-2\right)\left(x+2\right)\) với \(x=1\)
d) \(D=\left(x-3\right)\left(x+3\right)+\left(x-2\right)^2-2x\left(x-4\right)\) với \(x=-1\)
3/
a/ \(A=\left(x-y\right)^2+\left(x+y\right)^2.\)
\(A=\left(x^2-2xy+y^2\right)+\left(x^2+2xy+y^2\right)\)
\(A=x^2-2xy+y^2+x^2+2xy+y^2\)
\(A=2x^2+2y^2\)
b/ \(B=\left(2a+b\right)^2-\left(2a-b\right)^2\)
\(B=\left(4a^2+4ab+b^2\right)-\left(4a^2-4ab+b^2\right)\)
\(B=4a^2+4ab+b^2-4a^2+4ab-b^2\)
\(B=8ab\)
c/ \(C=\left(x+y\right)^2-\left(x-y\right)^2\)
\(C=\left(x^2+2xy+y^2\right)-\left(x^2-2xy+y^2\right)\)
\(C=x^2+2xy+y^2-x^2+2xy-y^2\)
\(C=4xy\)
d/ \(D=\left(2x-1\right)^2-2\left(2x-3\right)^2+4\)
\(D=\left(4x^2-4x+1\right)-2\left(4x^2-12x+9\right)+4\)
\(D=4x^2-4x+1-8x^2+24x-18+4\)
\(D=-4x^2+20x-13\)
Bài 3 :
\(a,A=\left(x-y\right)^2+\left(x+y\right)^2\)
\(=x^2-2xy+y^2+x^2+2xy+y^2\)
\(=2x^2+2y^2\)
\(b,B=\left(2a+b\right)^2-\left(2a-b\right)^2\)
\(=4a^2+4ab+b^2-4a^2+4ab-b^2\)
\(=8ab\)
\(c,C=\left(x+y\right)^2-\left(x-y\right)^2\)
Tương tự bài câu B
\(=4xy\)
\(d,D=\left(2x-1\right)^2-2\left(2x-3\right)^2+4\)
\(=4x^2-4x+1-2\left(4x^2-12x+9\right)+4\)
\(=4x^2-4x+1-8x^2+24x-18+4\)
\(=-4x^2+20x-13\)
\(a,A=\left(x-y\right)^2+\left(x+y\right)^2\)
\(A=2x^2+2y^2\)
\(b,B=2b^2\)
\(c,C=2y^2\)
Bài 3: a) A = (x - y)2 + (x + y)2 = x2 - 2xy + y2 + x2 + 2xy + y2 = 2x2 + 2y2
b) (2a + b)2 - (2a - b)2 = (2a + b - 2a + b)(2a + b + 2a - b) = 2b.4a = 8ab
c) (x + y)2 - (x -y)2 = (x + y - x + y)(x + y +x - y) = 2y.2x = 4xy
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 - 12
Bài 4: a) A = (x + 3)2 + (x - 3)(x + 3) - 2(x + 2)(x - 4)
A = x2 + 6x + 9 + x2 - 9 - 2(x2 - 4x + 2x - 8)
A = 2x2 + 6x - 2x2 + 4x + 16
A = 10x + 16
=> A = 10.(-1/2) + 16 = 11
b) B = (3x + 4)2 - (x - 4)(x + 4) - 10x = 9x2 + 24x + 16 - x2 + 16 - 10x = 8x2 + 12x + 32
=> B = 8.(-1/10)2 + 12.(-1/10) + 32 = 2/25 - 6/5 + 32 = 772/25
c) C = (x + 1)2 - (2x - 1)2 + 3(x - 2)(x + 2)
C = x2 + 2x + 1 - 4x2 + 4x - 1 + 3x2 - 12
C = 6x - 12
=> C = 6.1 - 12 = 6 -12 = -6
d) D = (x - 3)(x + 3) + (x - 2)2 - 2x(x - 4)
D = x2 - 9 + x2 - 4x + 4 - 2x2 + 8x
D = 4x - 5
=> D = 4.(-1) -5 = -4 - 5 = -9
Bài 4 ;
\(a,A=\left(x+3\right)^2+\left(x-3\right)\left(x+3\right)-2\left(x+2\right)\left(x-4\right)\)
\(=x^2+6x+9+x^2-9-2\left(x^2-2x-8\right)\)
\(=2x^2+6x-2x^2+4x+16\)
\(=10x+16\)
Thay \(x=-\frac{1}{2}\)vào bt A ta được :
\(A=10\cdot\left(-\frac{1}{2}\right)+16\)
\(=-5+16=11\)
\(b,B=\left(3x+4\right)^2-\left(x-4\right)\left(x+4\right)-10x\)
\(=9x^2+24x+16-x^2+16-10x\)
\(=8x^2-14x+32\)
\(=8\cdot\left(-\frac{1}{10}\right)-14\cdot\left(-\frac{1}{10}\right)+32=\frac{163}{5}\)
\(c,C=x^2+2x+1-4x^2+4x-1+3x^2-12\)
\(=6x-12\)
\(=6-12=-6\)
\(d,D=x^2-9+x^2-4x+4-2x^2+8\)
\(=-4x+3\)
\(=4-3=1\)
4/
a/ \(A=\left(x+3\right)^2+\left(x-3\right)\left(x+3\right)-2\left(x+2\right)\left(x-4\right).\)
\(A=x^2+6x+9+x^2-9-2\left(x^2-4x+2x-8\right)\)
\(A=x^2+6x+9+x^2-9-2x^2+8x-4x+16\)
\(A=10x+16\) thay x = -1/2
\(A=10\cdot-\frac{1}{2}+16=11\)
b/ \(\left(3x+4\right)^2-\left(x-4\right)\left(x+4\right)-10x\)
\(=9x^2+24x+16-\left(x^2-16\right)-10x\)
\(=9x^2+24x+16-x^2+16-10x\)
\(=8x^2+14x+32\)
thay x= -1/10
\(=8\cdot\left(-\frac{1}{10}\right)^2+14\cdot\left(-\frac{1}{10}\right)+32\)
\(=\frac{2}{25}-\frac{7}{5}+32=\frac{767}{25}\)
c/ \(C=\left(x+1\right)^2-\left(2x-1\right)^2+3\left(x-2\right)\left(x+2\right)\)
\(C=x^2+2x+1-\left(4x^2-2x+1\right)+3\left(x^2-4\right)\)
\(C=x^2+2x+1-4x^2+2x-1+3x^2-12\)
\(C=4x-12\) thay x=1
\(C=4\cdot1-12=-8\)
d/ \(D=\left(x-3\right)\left(x+3\right)+\left(x-2\right)^2-2x\left(x-4\right)\)
\(D=x^2-9+x^2-2x+4-2x^2+8x\)
\(D=6x-5\) thay x= -1
\(D=6\cdot\left(-1\right)-5=-11\)
Bài 3:
a, \(A=\left(x-y\right)^2+\left(x+y\right)^2\)
\(=x^2-2xy+y^2+x^2+2xy+y^2\)
\(=2x^2+2y^2\)
\(=2\left(x^2+y^2\right)\)( Rút gọn thế này đc chưa :V )
b, \(B=\left(2a+b\right)^2-\left(2a-b\right)^2\)
\(=4a^2+2\cdot2a\cdot b+b^2-4a^2+2\cdot2a\cdot b-b^2\)
\(=\left(4a^2-4a^2\right)+\left(b^2-b^2\right)+4ab+4ab\)
\(=8ab\)
c, \(C=\left(x+y\right)^2-\left(x-y\right)^2\)
\(=x^2+2xy+y^2-x^2+2xy-y^2\)
\(=2xy+2xy\)
\(=4xy\)
d, \(D=\left(2x-1\right)^2-2\left(2x-3\right)^2+4\)
\(=4x^2-4x-2\cdot\left(4x^2-12x+9\right)+4\)
\(=4x^2-4x-8x^2+24x-18+4\)
\(=-4x^2+20x-14\)
P/s: Chả chắc đc câu nào 100% :v Rối. Bài 4 sẽ có trong ít phút nữa :)
