Question
Factorise : $\left(a^2-b^2\right)\left(c^2-d^2\right)-4 a b c d$
✓
Answer
$(a c-b d+a d+b c)(a c-b d-a d-b c)$
[Hint. Given Exp. $\left.=(a c-b d)^2-(a d+b c)^2\right]$
[Hint. Given Exp. $\left.=(a c-b d)^2-(a d+b c)^2\right]$
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
Show that the points A (1, 1), B (-1, 5), C (7, 9) and D (9, 5) are the vertices of a rectangle ABCD.
[Hint. Show that AB = CD, BC = AD and diag. AC = diag. BD.]
[Hint. Show that AB = CD, BC = AD and diag. AC = diag. BD.]
Factorise : $x(x-2)-y(y-2)$
→$\text{ABCDE}$ is the end view of a factory shed which is $50\ m$ long. The roofing of the shed consists of asbestos sheets as shown in the figure. The two ends of the shed are completely closed by brick walls.
Calculate the total volume content of the shed.
→Calculate the total volume content of the shed.
Simple interest on a sum of money for $2$ years at $4\%$ is $Rs .450.$ Find compound interest on the same sum and at the same rate for $1$ year, if the interest is reckoned half yearly.
→If $\sec \theta=\frac{13}{5}$, show that $\left(\frac{2 \sin \theta-3 \cos \theta}{4 \sin \theta-9 \cos \theta}\right)=3$.
→Evaluate the following:
$(9)^{\frac{5}{2}}-3 .(4)^0-\left(\frac{1}{81}\right)^{-\frac{1}{2}}$
→$(9)^{\frac{5}{2}}-3 .(4)^0-\left(\frac{1}{81}\right)^{-\frac{1}{2}}$
Solve the following equations for the unknown$: 8x - 21 = 3x - 11$
→
In the given figure, ABCD is a piece of cardboard in the shape of a trapezium in which AB || DC, $\angle$ABC = $90^{\circ}$. From this piece, quarter circle BEFC is removed. Given DC = BC = 4.2cm and AE = 2cm.
Calculate the area of the remaining piece of the cardboard.
[Hint. Required Area
= (Area of trap. ABCD) - (Area of quadrant BEFC).]
Find two rational numbers between: -2 and 1
In the given figure, $AB$ and $EC$ are parallel to each other. Sides $AD$ and $BC$ are $2 \ cm$ each and are perpendicular to $AB.$
Given that $\angle AED = 60^\circ $ and $\angle ACD = 45^\circ .$ Calculate$: AB.$
→Given that $\angle AED = 60^\circ $ and $\angle ACD = 45^\circ .$ Calculate$: AB.$