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\(A\cdot B=\left(2x^2+3x+5\right)\left(x^2-x+3\right)=2x^4-2x^3+6x^2+3x^3-3x^2+9x+5x^2-5x+15\)
\(A\cdot B=2x^4+x^3+8x^2+4x+15\)
A.B = (2x2 + 3x + 5).(x2 - x + 3)
= 2x2.x2 - 2x2.x + 2x2.3 + 3x.x2 - 3x.x +3x.3 + 5.x2 - 5.x + 5.3
= 2x4 - 2x3 + 6x2 + 3x3 - 3x2 + 9x + 5x2 - 5x + 15
= 2x4 - (2x3 - 3x3) + (6x2 - 3x2 + 5x2) + (9x - 5x) +15
= 2x4 + x3 + 8x2 + 4x +15
C1
a) -7x(3x-2)=-21x^2+14x
b) 87^2+26.87+13^2=87^2+2.13.87+13^2=(87+13)^2=100^2
C2
a) (x-5)(x+5)
b)3x(x+5)-2(x+5)=(3x-2)(x+5)=0
\(\Rightarrow\left[\begin{array}{nghiempt}3x-2=0\\x+5=0\end{array}\right.\)
\(\Rightarrow\left[\begin{array}{nghiempt}x=\frac{2}{3}\\x=-5\end{array}\right.\)
Vậy S={-5;2/3}
C3:
a)3x^3-2x^2+2=(x+1)(3x^2-5x-5)-3
b) Để A chia hết cho B=> x+1\(\inƯ\left(-3\right)\)
\(\Rightarrow\begin{cases}x+1=3\\x+1=-3\\x+1=1\\x+1=-1\end{cases}\)\(\Rightarrow\begin{cases}x=2\\x=-4\\x=0\\x=-2\end{cases}\)
(3 - 2x)(x2 - 2xy + 1) = 3x2 - 6xy + 3 - 2x3 + 4x2y - 2x
a. 2x^2 ( 5x^3 - 4x^2 - 7xy + 1 )
= 10x^5 - 8x^4 - 14x^3y + 1
b. ( x - 5 ) ( x + 3 )
= x^2 + 3x - 5x - 15
= x^2 - 2x - 15
c. ( x - 1 ) ( x + 2 )
= x^2 + 2x - x - 2
= x^2 - x - 2
d. ( 2x + y ) ( 2x - y )
= 4x^2 - 2xy + 2xy - y^2
= 4x^2 - y^2
a) \(2x^2\left(5x^3-4x^2.g-7xy+1\right)\)
\(=10x^5-8x^4.g-14x^3y+2x^2\)
b) \(\left(x-5\right)\left(x+3\right)\)
\(=x^2+3x-5x-15\)
\(=x^2-2x-15\)
c) \(\left(x-1\right)\left(x+2\right)\)
\(=x^2+2x-x-2\)
\(=x^2+x-2\)
d) \(\left(2x+y\right)\left(2x-y\right)\)
\(=4x^2-y^2\)
a) (2x - 1)2 - (x + 3)2
= (2x - 1 - x - 3).(2x - 1 + x + 3)
= (x - 4).(3x + 2)
b) x2.(x - 3) + 12 - 4x
= x2.(x - 3) - 4x + 12
= x2.(x - 3) - 4.(x - 3)
= (x - 3).(x2 - 4)
= (x - 3).(x - 2).(x + 2)
Áp dụng HĐT:
a2 - b2 = (a - b)(a + b)
\(\left(2x-1\right)^2-\left(x+3\right)^2\)
\(=\left(2x-1-x-3\right)\left(2x-1+x+3\right)\)
\(=\left(x-4\right)\left(3x+2\right)\)
(5x - 2y)(x2 - xy + 1)
= 5x3 - 5x2y + 5x - 2x2y + 2xy2 - 2y
= 5x3 - 7x2y + 2xy2 + 5x - 2y
(x - 1)(x + 1)(x + 2)
= (x2 - 1)(x + 2)
= x3 + 2x2 - x - 2
1/2x2y2(2x + y)(2x - y)
= 1/2x2y2(4x2 - y2)
= 2x4y2 - 1/2x2y4
http://123link.pro/Hya7
(x+10)(x-2)+x(x2-3)
=x^2 -2x+10x-20+x^3-3x
=x^3+x^2+5x-20