Question

phân tích đa thức thành nhân tử :A=4x^4+625

Answer 1

\(4x^4+625=\left(2x^2\right)^2+\left(5^2\right)^2=\left(2x^2\right)^2+2.2x^2.5^2+\left(5^2\right)^2-2.2x^2.5^2\)

\(=\left(2x^2+25\right)^2-100x^2=\left(2x^2+25-10x\right)\left(2x^2+25+10x\right)\)

Answer 2

\(4x^4+625\)

\(=4x^4+20x^3-20x^3+50x^2+50x^2-100x^2-250x+250x+625\)

\(=\left(4x^4+20x^3+50x^2\right)-\left(20x^3-100x^2-250x\right)+\left(50x^2+250x+625\right)\)

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

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