Question
Factorize the following expressions:
$x^4y^4 - xy$
$x^4y^4 - xy$
✓
Answer
$x^4 y^4-x y \\$
$=x y\left(x^3 y^3-1\right) \\$
$=x y\left((x y)^3-1^3\right) \\$
$=x y(x y-1)\left((x y)^2+x y \times 1+12\right) \\ {\left[\therefore x^3-y^3=(x-y)\left(x^2+x y+y^2\right)\right]} \\$
$=x y(x y-1)\left(x^2 y^2+x y+1\right) \\$
$\therefore x^4 y^4-x y=x y(x y-1)\left(x^2 y^2+x y+1\right)$
$=x y\left(x^3 y^3-1\right) \\$
$=x y\left((x y)^3-1^3\right) \\$
$=x y(x y-1)\left((x y)^2+x y \times 1+12\right) \\ {\left[\therefore x^3-y^3=(x-y)\left(x^2+x y+y^2\right)\right]} \\$
$=x y(x y-1)\left(x^2 y^2+x y+1\right) \\$
$\therefore x^4 y^4-x y=x y(x y-1)\left(x^2 y^2+x y+1\right)$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Simplify the following products:$(\text{x}^2 +\text{x}- 2)(\text{x}^2-\text{x} + 2)$
→Radius of a circle is $34\ cm$ and the distance of the chord from the centre is $30\ cm$ , find the length of the chord.
Given: in a circle with centre $A$,
$P A$ is radius and PQ is chord,
seg $AM \perp$ chord PQ , $P - M - Q$
$AP =34 cm, AM =30 cm$
To Find: Length of the chord (PQ)
→Given: in a circle with centre $A$,
$P A$ is radius and PQ is chord,
seg $AM \perp$ chord PQ , $P - M - Q$
$AP =34 cm, AM =30 cm$
To Find: Length of the chord (PQ)
Prove that the quadrilateral formed by joining the midpoints of sides of a quadrilateral in order is a parallelogram.
Express the following decimals in the form $\frac{\text{p}}{\text{q}},$ where p, q are integers and $\text{q}\neq0.$$0.\overline{2}$
→In the given figure, if ∠a = ∠b then prove that line l || line m.
Given: ∠a ≅ ∠b
To prove: line l| line m
Factorise:$\sqrt{5}\text{x}^2+2\text{x}-3\sqrt{5}$
→Water in a rectangular reservoir having base $80\ m$ by $60\ m$ is $6.5\ m$ deep. In what time can the water be pumped by a pipe of which the cross-section is a square of side $20\ cm$ if the water runs through the pipe at the rate of $15\ km/hr.$
→The angles of a triangles are in the ratio $2: 3: 4$ Find the angles.
→Given that $1$ cubic cm of marble weighs $0.25kg$, the weight of marble block $28cm$ in width and $5cm$ thick is $112kg$. Find the length of the block.
→The areas of three adjacent faces of a cuboid are x, y and z. If the volume is V, Prove that $V^2 = xyz.$
→