Question
Factorise: $a^4-2 a^2 b^2+b^4$
✓
Answer
$a^4-2 a^2 b^2+b^4$
$a^4-2 a^2 b^2+b^4$ $=\left(a^2\right)^2-2\left(a^2\right)\left(b^2\right)+\left(b^2\right)^2$
$ =\left(a^2-b^2\right)^2. . . .$ [Using Identity $II$
$=\left\{(a-b)(a+b)^2\right\}. . . .$ [Using Identity $III$
$=(a-b)^2(a+b)^2$.
$a^4-2 a^2 b^2+b^4$ $=\left(a^2\right)^2-2\left(a^2\right)\left(b^2\right)+\left(b^2\right)^2$
$ =\left(a^2-b^2\right)^2. . . .$ [Using Identity $II$
$=\left\{(a-b)(a+b)^2\right\}. . . .$ [Using Identity $III$
$=(a-b)^2(a+b)^2$.
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
By taking three different values of n verify the truth of the following statement: If n leaves remainder $1$ when divided by $3$, then $n^3$ also leaves $1$ as remainder when divided by $3.$
→Check, whether 180 is a perfect square or not using prime factorisation.
Observe the multiplication grid below. Each number inside the grid is formed by multiplying two numbers. If the middle number of a 3 × 3 frame is given by the expression pq, as shown in the figure, write the expressions for the other numbers in the grid.
The dimensions of a metal block are $2.25\ m$ by $1.5\ m$ by $27\ cm$. It is melted and recast into cubes, each of the side $45\ cm.$ How many cubes are formed$ ?$
→Water flows from a tank with a rectangular base measuring $80\ cm$ by $70\ cm$ into another tank with a square base of side $60\ cm$. If the water in the first tank is $45\ cm$ deep, how deep will it be in the second tank?
→Find the rate at which a sum of money will double itself in $3$ years, if the interest is compounded annually.
→Solve: $\frac{7\text{y}+4}{\text{y}+7}=\frac{-4}{3}$
→Solve:
$ 49-a^2+8 a b-16 b^2 $
→$ 49-a^2+8 a b-16 b^2 $
One fruit salad recipe requires $\frac{1}{2}$ cup of sugar. Another recipe for the same fruit salad requires $2$ tablespoons of sugar. If $1$ tablespoon is equivalent to $\frac{1}{16}$ cup, how much more sugar does the first recipe require?
→Find the product: $\big(−\frac{7}{4}\text{ab}^2\text{c}−\frac{6}{25}\text{a}^2\text{c}^2\big)\big(−50\text{a}^2\text{b}^2\text{c}^2\big)$
→