Question

m^4-18m^2n^2+81n^4 factorise

Answer 1

${m}^{4} - 18 {m}^{2} {n}^{2} + 81 {n}^{4} \\ = {( {m}^{2} - 9 {n}^{2} )}^{2} \\ = {(m + 3n)}^{2} {(m - 3n)}^{2}$

Answer 2

Factorisation,

We have,
${m}^{4} - 18 {n}^{2} {m}^{2} + 81 {n}^{4}$

= m⁴ - 9m².n²- 9m².n²+ 81n⁴

= m²(m²- 9n²) - 9n²(m²-9n²)

= (m²-9n²)(m²- 9n²)

= {m²- (3n)²}{m²- (3n)²}

= (m + 3n)(m - 3n)(m + 3n)(m - 3n)

Or you can do it in this way,
Using the formula,a²-2ab+b² = (a-b)²
ok,

Now,
${m}^{4} - 18 {n}^{2} {m}^{2} + 81 {n}^{4}$

= (m²)²-2×9n×m + (9n²)²

= (m²- 9n²)²

= (m²-9n²)(m²- 9n²)

= {m²- (3n)²}{m²- (3n)²}

= (m + 3n)(m - 3n)(m + 3n)(m - 3n)

That's it
Hope it helped (*^_^*)