Question

Factorise
question
ii
v
viii

Answer 1

$\boxed{\underline{\textsf{Solution :}}}$

$\boxed{(ii)}$

Now, (l + m)² - (l - m)²

= {(l+ m) + (l - m)} {(l + m) - (l - m)}

since a² - b² = (a + b) (a - b)

= {l + m + l - m} {l + m - l + m}

= 2l * 2m

= 4lm ,

which is the required factorization.

$\underline{\textsf{Another method :}}$

Now, (l + m)² - (l - m)²

since (a + b)² = a² + 2ab + b²

and (a - b)² = a² - 2ab + b²

= (l² + 2lm + m²) - (l² - 2lm + m²)

= l² + 2lm + m² - l² + 2lm - m²

= 4lm ,

which is the required factorization.

$\boxed{(v)}$

Now, x⁴ + 8x²y² + 16y⁴ - 9z⁴

= {(x²)² + (2 * x² * 4y²) + (4y²)²} - (3z²)²

= (x² + 4y²)² - (3z²)²

since a² + 2ab + b² = (a + b)²

= (x² + 4y² + 3z²) (x² + 4y² - 3z²) ,

since a² - b² = (a + b) (a - b)

which is the required factorization.

$\boxed{(viii)}$

Now, 48a² - 243b²

= 3 (16a² - 81b²)

= 3 {(4a)² - (9b)²}

= 3 (4a + 9b) (4a - 9b) ,

since a² - b² = (a + b) (a - b)

which is the required factorization.

Answer 2

Answer:

ii.given

viii. given

Step-by-step explanation:

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