Question

factories the following.(1)a⁴-b⁴​

Answer 1

Answer:

=(a^2) ^2-(b^2) ^2

=(a^2+b^2) (a^2-b^2)

Answer 2

(a+b) × (a-b) × (a²+b²)

• Here, we are asked to factorise the given equation.

EquatioN giveN -

$\qquad\quad\bigstar\; \sf{{a}^{4}-{b}^{4}}$

We can write a⁴-b⁴ as (a²)²- (b²)². So,

$\dashrightarrow\quad\sf{{a}^{4}-{b}^{4}={({a}^{2})}^{2}-{({b}^{2})}^{2}}$

Now, -

The equation is in the firm of a²-b². We know, that a²-b² = (a+b) (a-b). So,

$\dashrightarrow\quad\sf{{a}^{4}-{b}^{4}=({a}^{2}-{b}^{2})\: ({a}^{2}+{b}^{2})}$

Using a²-b² again.

$\dashrightarrow\quad\red{\sf{{a}^{4}-{b}^{4}=(a+b)\times (a-b)\times ({a}^{2}+{b}^{2})}}$

FinaL answEr -

$\qquad\leadsto\quad$ a⁴ - b⁴ = (a + b) × (a - b) × (a² + b²)