Question

Viết các biểu thức sau dưới dạng tích :

a. \(9.x^2+30x+25\)            

b. \(\dfrac{4}{9}.x^{^{ }4}-16x^2\)

c. \(a^2y^2+b^2x^2-2axby\)         

d. \(100-\left(3x-y\right)^2\)

e. \(\dfrac{12}{5}x^2y^2-9x^4-\dfrac{4}{25}y^4\)

f.\(64x^2-\left(8a+b\right)^2\)

g.\(27x^3-a^3b^3\)

Answer 1

a. \(9x^2+30x+25=\left(3x+5\right)^2\)

b. \(\dfrac{4}{9}x^4-16x^2=\left(\dfrac{2}{3}x^2-4x\right)\left(\dfrac{2}{3}x^2+4x\right)=x^2\left(\dfrac{2}{3}x-4\right)\left(\dfrac{2}{3}x+4\right)\)

c. \(a^2y^2+b^2x^2-2axby=\left(ay-bx\right)^2\)

d. \(100-\left(3x-y\right)^2=\left(10-3x+y\right)\left(10+3x-y\right)\)

e. \(\dfrac{12}{5}x^2y^2-9x^4-\dfrac{4}{25}y^4=-\left(9x^4-\dfrac{12}{5}x^2y^2+\dfrac{4}{25}y^4\right)=-\left(3x^2-\dfrac{2}{5}y^2\right)^2\)

f. \(64x^2-\left(8a+b\right)^2=\left(8x-8a-b\right)\left(8x+8a+b\right)\)

g. \(27x^3-a^3b^3=\left(3x-ab\right)\left(9x^2+3xab+a^2b^2\right)\)