c) Ta có: \(33\cdot55+33\cdot67+45\cdot33+67\cdot67\)

\(=33\left(55+45\right)+67\left(33+67\right)\)

\(=33\cdot100+67\cdot100\)

\(=100\cdot100=10000\)

chỉ biết lm câu b thôi

5+10+15+20+25+30+35+40+45+50=5.(1+2+3+4=5+6+7+8+9+10)=55.5=5x50x5=250.5=1250

2)Tính nhanh:

a)\(202^2-54^2+256.352\)

​\(=\left(202-54\right)\left(202+54\right)+256.352\)​

\(=148.256+256.352\)

\(=256\left(148+352\right)\)

\(=256.500\)

\(=128000\)

b)\(621^2-769.373-148^2\)

\(=621^2-148^2-769.373\)

\(=\left(621-148\right)\left(621+148\right)-769.373\)

\(=473.769-769.373\)

\(=769\left(473-373\right)\)

\(=769.100\)

\(=76900\)

\(a,\left(x-y+4\right)^2-\left(2x+3y-1\right)^2\)

\(=\left(x-y+4-2x-3y+1\right)\left(x-y+4+2x+3y-1\right)\)

\(=\left(-x-4y+5\right)\left(3x+2y+3\right)\)

\(b,9x^2+90x+225-\left(x-7\right)^2\)

\(=9\left(x^2+10x+25\right)-\left(x-7\right)^2\)

\(=9\left(x+5\right)^2-\left(x-7\right)^2\)

\(=\left[3\left(x+5\right)\right]^2-\left(x-7\right)^2\)

\(=\left(3x+15\right)^2-\left(x-7\right)^2\)

\(=\left(3x+15-x+7\right)\left(3x+15+x-7\right)\)

\(=\left(2x+22\right)\left(4x+8\right)\)

\(=2\left(x+11\right).4\left(x+2\right)\)

\(=8\left(x+2\right)\left(x+11\right)\)

\(c,49\left(y-4\right)^2-9y^2-36y-36\)

\(=\left\{\left[7\left(y-4\right)\right]^2-\left(3y\right)^2\right\}-\left(36y+36\right)\)

\(=\left(7y-28-3y\right)\left(7y-28+3y\right)-36\left(y+1\right)\)

\(=\left(4y-28\right)\left(10y-28\right)-36\left(y+1\right)\)

\(=4\left(y-7\right)2\left(5y-14\right)-36\left(y+1\right)\)

\(=8\left(y-7\right)\left(5y-14\right)-36\left(y+1\right)\)

\(=4\left[2\left(y-7\right)\left(5y-14\right)-9\left(y+1\right)\right]\)

mk ko chắc là câu này mk lm đg

\(d,x^2-5x-14\)

\(=x^2+2x-7x-14\)

\(=x\left(x+2\right)-\left(7x+14\right)\)

\(=x\left(x+2\right)-7\left(x+2\right)\)

\(=\left(x+2\right)\left(x-7\right)\)

\(x^2+7x+12=x^2+3x+4x+12=x\left(x+3\right)+4\left(x+3\right)=\left(x+3\right)\left(x+4\right)=0\)

\(x^2+3x-18=0\Leftrightarrow x^2-3x+6x-18=x\left(x-3\right)+6\left(x-3\right)=\left(x+6\right)\left(x-3\right)=0\)

b) \(x^2-10x+16\)

\(=x^2-2x-8x+16\)

\(=x\left(x-2\right)-8\left(x-2\right)\)

\(=\left(x-2\right)\left(x-8\right)\)

c) \(x^2+6x+8\)

\(=x^2+2x+4x+8\)

\(=x\left(x+2\right)+4\left(x+2\right)\)

\(=\left(x+2\right)\left(x+4\right)\)

d) tươn tự c

e) \(x^2+3x-18=0\)

\(\Leftrightarrow x^2+6x-3x-18=0\)

\(\Leftrightarrow x\left(x+6\right)-3\left(x+6\right)=0\)

\(\Leftrightarrow\left(x+6\right)\left(x-3\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x+6=0\\x-3=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-6\\x=3\end{cases}}}\)

Vậy ,...

f) \(8x^2+30x+7=0\)

\(\Leftrightarrow8x^2+28x+2x+7=0\)

\(\Leftrightarrow4x\left(2x+7\right)+\left(2x+7\right)=0\)

\(\Leftrightarrow\left(2x+7\right)\left(4x+1\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}2x+7=0\\4x+1=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=\frac{-7}{2}\\x=\frac{-1}{4}\end{cases}}}\)

Vậy ...

g) \(x^3-11x^2+30x=0\)

\(\Leftrightarrow x^3-5x^2-6x^2+30x=0\)

\(\Leftrightarrow x^2\left(x-5\right)-6x\left(x-5\right)=0\)

\(\Leftrightarrow\left(x-5\right)\left(x^2-6x\right)=0\)

\(\Leftrightarrow x\left(x-5\right)\left(x-6\right)=0\)

\(\Leftrightarrow x=0\)hoặc x=5 hoặc x=6

Vậy ...