Question

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Answer 1

Answer:

1)7x-y

2)2p+2p square

3) 2a square +b square -2a square +2b square

Answer 2

3. The simplified form of the given expressions are :

i) 7x² - 6xy - y²

ii) 2 (p - q) (p² + q² + pq)

iii) 4a²b²

3.i) Given expression is :

(2x - 3y) (3x + y) + (x + 2y) (x - y)

= 2x (3x + y) - 3y (3x + y) + x (x - y) + 2y (x - y)

= 2x.3x + 2x.y - 3y.3x - 3y.y + x.x -x.y + 2y.x - 2y.y

= 6x² + 2xy - 9xy - 3y² + x² - xy + 2yx - 2y²

= (6x² + x²) + (2xy - 9xy - xy + 2yx) - (3y² - 2y²)

= 7x² - 6xy - y²

• Therefore, (2x - 3y) (3x + y) + (x + 2y) (x - y) = 7x² - 6xy - y²

3.iv) Given expression is :

(p + q) (p² - q²) + (p - q) (p² + q²)

Applying the formula p² - q² = (p + q) (p - q), we get,

(p + q) (p + q) (p - q) + (p - q) (p² + q²)

Taking out (p - q) as the common factor,

(p - q) { (p + q) (p + q) + (p² + q²) }

= (p - q) { (p + q)² + (p² + q²) }

Applying the formula (p + q)² = p² + q² + 2pq,

(p - q) { (p² + q² + 2pq) + (p² + q²) }

= (p - q) (p² + q² + 2pq+ p² + q²)

= (p - q) ( 2p² + 2q² + 2pq)

Taking out 2 as the common factor,

(p - q) × 2 (p² + q² + pq)

= 2 (p - q) (p² + q² + pq)

• Therefore, (p + q) (p² - q²) + (p - q) (p² + q²) = 2 (p - q) (p² + q² + pq)

3.vi) Given expression is :

(a² + b²) (a² + b²) - (a² - b²) (a² - b²)

= (a² + b²)² - (a² - b²)²

Applying the formula (x + y)² = x² + y² + 2xy, and (x - y)² = x² + y² - 2xy, and considering x = a² and y = b² :

{ (a²)² + (b²)² + 2a²b² } - { (a²)² + (b²)² - 2a²b² }

= (a⁴ + b⁴ + 2a²b²) - (a⁴ + b⁴ - 2a²b²)

= a⁴ + b⁴ + 2a²b² - a⁴ - b⁴ + 2a²b²

= a⁴ - a⁴ + b⁴ - b⁴ + 2a²b² + 2a²b²

= 4a²b²

• Therefore, (a² + b²) (a² + b²) - (a² - b²) (a² - b²) = 4a²b²