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\(a,5xy\left(-7x^3y^4\right)\)
\(=5\left(-7\right)\left(xx^3\right)\left(yy^4\right)\)
\(=-35x^4y^5\)
Hệ số: -35.
Bậc: 9.
Các câu còn lại lm tương tự nhá.
hok tốt!
\(\frac{8^2.4^3}{16^3}=\frac{\left(2^3\right)^2.\left(2^2\right)^3}{\left(2^4\right)^3}=\frac{2^6.2^6}{2^{12}}=1\)
\(\frac{25^2.125}{5^3.5^4}=\frac{\left(5^2\right)^2.5^3}{5^4.5^3}=\frac{5^4.5^3}{5^4.5^3}=1\)
\(\frac{8^2.4^3}{16^3}=\frac{\left(2^3\right)^2.\left(2^2\right)^3}{\left(2^4\right)^3}=\frac{2^6.2^6}{2^{12}}=1\)
\(\frac{25^2.125}{5^3.5^4}=\frac{\left(5^2\right)^2.5^3}{5^3.5^4}=\frac{5^4.5^3}{5^3.5^4}=1\)
\(4x^4-21x^2y^2+y^4\)
\(=\left(4x^4+4x^2y^2+y^4\right)-25x^2y^2\)
\(=\left(2x^2+y^2\right)^2-\left(5xy\right)^2\)
\(=\left(2x^2+y^2-5xy\right)\left(2x^2+y^2+5xy\right)\)
\(a,4x^4-21x^2y^2+y^4=\left(2x^2\right)^2+4x^2y^2+y^4-4x^2y^2-21x^2y^2\)
\(=\left(2x^2+y^2\right)^2-25x^2y^2\)
\(=\left(2x^2+y^2-5xy\right)\left(2x^2+y^2+5xy\right)\)
\(b,x^5-5x^3+4x=x\left(x^4-5x^2+4\right)\)
\(=x\left(x^4-4x^2-x^2+4\right)\)
\(=x\left[x^2\left(x^2-4\right)-\left(x^2-4\right)\right]\)
\(=x\left(x^2-4\right)\left(x^2-1\right)\)
\(=x\left(x-2\right)\left(x+2\right)\left(x-1\right)\left(x+1\right)\)
\(c,x^3+5x^2+3x-9=x^3-x^2+6x^2-6x+9x-9\)
\(=x^2\left(x-1\right)+6x\left(x-1\right)+9\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2+6x+9\right)\)
\(=\left(x-1\right)\left(x^2+3x+3x+9\right)\)
\(=\left(x-1\right)\left[x\left(x+3\right)+3\left(x+3\right)\right]\)
\(=\left(x-1\right)\left(x+3\right)\left(x+3\right)\)
\(=\left(x-1\right)\left(x+3\right)^2\)
\(d,x^{16}+x^8-2=x^{16}+2x^8-x^8-2\)
\(=x^8\left(x^8-1\right)+2\left(x^8-1\right)\)
\(=\left(x^8-1\right)\left(x^8+2\right)\)
\(2^2-\left(-3^2\right)^3+\frac{16}{4^2}-2.5^2\)
\(=2^2+3^6+1-2.25\)
\(=4+729+1-50\)
\(=684\)