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1 If we continue polluting the air, the environment will be affected seriously
2 If we don't stop damaging birds' homes, there will be fewer birds left
3 If we continue polluting the water, there will be more disease in people and animals
4 If we keep polluting the land, the soil will not be safe enough for us to grow food in
5 If we use public transportation when we need, there will be less air pollution
12 Daniel signs up for a clean-up campaign so that he can join in it
13 People in my neighborhood clean the park up so that their children will have a nice place to play
14 Almost all the students in my school plant trees so that they can have much fresher air
e: \(\dfrac{x^2+3x+9}{x^3+4x^2+4x}\cdot\dfrac{x^2+2x}{x^3-27x}\)
\(=\dfrac{x^2+3x+9}{x\left(x^2+4x+4\right)}\cdot\dfrac{x\left(x+2\right)}{x\left(x^2-27\right)}\)
\(=\dfrac{x^2+3x+9}{\left(x+2\right)^2}\cdot\dfrac{x+2}{x\left(x^2-27\right)}\)
\(=\dfrac{\left(x^2+3x+9\right)}{\left(x+2\right)\cdot x\left(x^2-27\right)}\)
f: \(\dfrac{2x^2+4xy+2y^2}{5x-5y}\cdot\dfrac{15x-15y}{2x^3+2y^3}\)
\(=\dfrac{2\left(x^2+2xy+y^2\right)}{5\left(x-y\right)}\cdot\dfrac{15\left(x-y\right)}{2\left(x^3+y^3\right)}\)
\(=\dfrac{\left(x+y\right)^2}{1}\cdot\dfrac{3}{\left(x+y\right)\left(x^2-xy+y^2\right)}\)
\(=\dfrac{3\left(x+y\right)}{x^2-xy+y^2}\)
g: \(\dfrac{x^3-4x}{x^2-7x+12}\cdot\dfrac{x-4}{x^2-2x}\)
\(=\dfrac{x\left(x^2-4\right)}{\left(x-3\right)\left(x-4\right)}\cdot\dfrac{x-4}{x\left(x-2\right)}\)
\(=\dfrac{x^2-4}{\left(x-3\right)\left(x-2\right)}=\dfrac{\left(x-2\right)\left(x+2\right)}{\left(x-3\right)\left(x-2\right)}=\dfrac{x+2}{x-3}\)
\(x:y:z=\dfrac{4}{7}:\dfrac{5}{8}:\dfrac{9}{10}=160:175:252\)
\(4x^4+1\)
\(=4x^4+4x^2+1-4x^2\)
\(=\left(2x^2+1\right)^2-\left(2x\right)^2\)
\(=\left(2x^2+1+2x\right)\left(2x^2+1-2x\right)\)
\(4x^4+1=4x^4+4x^2+1-4x^2=\left(2x^2+1\right)^2-\left(2x\right)^2\)
\(=\left(2x^2-2x+1\right)\left(2x^2+2x+1\right)\)
1 If I were you I would recycle these plastic carrier bags
2 The pilots suddenly struck, so all flights had to be cancelled
3 The polluted environment causes the death of birds and plants
4 The contaminated food leads to people's poor health
a) \(f\left(x\right)+g\left(x\right)-h\left(x\right)\)
\(=\left(2x^5-4^4x^4+3x^3-x^2+5x-1\right)+\left(-x^5+2x^4-3x^3-x^2-2x+7\right)-\left(x^5-2x^4-2x^2-x-3\right)\)
\(=2x^5-4x^4+3x^3-x^2+5x-1-x^5+2x^4-3x^3-x^2-2x+7-x^5+2x^4+2x^2+x+3\)\(=\left(2x^5-x^5-x^5\right)-\left(4x^4-2x^4-2x^4\right)+\left(3x^3-3x^3\right)-\left(x^2+x^2-2x^2\right)+\left(5x-2x+x\right)-\left(1-7-3\right)\)
\(=0-0+0-0+4x-9\)
\(=4x-9\)
`a,`
`f(x)+g(x)-h(x)=(2x^5-4x^4+3x^3-x^2+5x-1)+(-x^5+2x^4-3x^3-x^2-2x+7)-(x^5-2x^4-2x^2-x-3)`
`= 2x^5-4x^4+3x^3-x^2+5x-1+ -x^5+2x^4-3x^3-x^2-2x+7-x^5+2x^4+2x^2+x+3`
`= (2x^5-x^5-x^5)-(4x^4-2x^4-2x^4)+(3x^3-3x^3)-(x^2-2x^2)-(2x-x)+(-1+7+3)`
`= 0-0+0-(-x^2)-x+10 = x^2-x+9`
m: \(=x^m\cdot x^2-x^m=x^m\left(x^2-1\right)=x^m\left(x-1\right)\left(x+1\right)\)
n: \(=5\cdot x^m\cdot x^2+10x^2\)
\(=5x^2\left(x^m+2\right)\)
o: \(=5x\left(x-2y\right)+2\left(x-2y\right)^2\)
\(=\left(x-2y\right)\left(5x+2x-4y\right)\)
=(x-2y)(7x-4y)
p: \(=7x\left(y-4\right)^2+\left(y-4\right)^3\)
\(=\left(y-4\right)^2\cdot\left(7x+y-4\right)\)
q: \(\left(4x-8\right)\left(x^2+6\right)-\left(4x-8\right)\left(x+7\right)+9\left(8-4x\right)\)
\(=\left(4x-8\right)\left(x^2+6-x-7\right)-9\left(4x-8\right)\)
\(=\left(4x-8\right)\left(x^2-x-10\right)\)
\(=4\left(x-2\right)\left(x^2-x-10\right)\)
m) \(x^{m+2}-x^m\)
\(=x^m\cdot x^2-x^m\)
\(=x^m\left(x^2-1\right)\)
\(=x^m\left(x^2-1^2\right)\)
\(=x^m\left(x-1\right)\left(x+1\right)\)
n) \(5x^{m+2}+10x^2\)
\(=5x^m\cdot x^2+10x^2\)
\(=5x^2\cdot x^m+10x^2\)
\(=5x^2\left(x^m+2\right)\)
o) \(5x\left(x-2y\right)+2\left(2y-x\right)^2\)
\(=5x\left(x-2y\right)+2\left(x-2y\right)^2\)
\(=\left(x-2y\right)\left[5x+2\left(x-2y\right)\right]\)
\(=\left(x-2y\right)\left(5x+2x-4y\right)\)
\(=\left(x-2y\right)\left(7x-4y\right)\)
p) \(7x\left(y-4\right)^2-\left(4-y\right)^3\)
\(=7x\left(4-y\right)^2-\left(4-y\right)^3\)
\(=\left(4-y\right)^2\left[7x-\left(4-y\right)\right]\)
\(=\left(4-y\right)^2\left(7x-4+y\right)\)
q) \(\left(4x-8\right)\left(x^2+6\right)-\left(4x-8\right)\left(x+7\right)+9\left(8-4x\right)\)
\(=4\left(x-2\right)\left(x^2+6\right)-4\left(x-2\right)\left(x+7\right)-36\left(x-2\right)\)
\(=4\left(x-2\right)\left[\left(x^2+6\right)-\left(x+7\right)-9\right]\)
\(=4\left(x-2\right)\left(x^2+6-x-7-9\right)\)
\(=4\left(x-2\right)\left(x^2-x-10\right)\)