Solve the question:(i) x2 + xy + 8x + 8y(ii) 15xy − 6x + 5y − 2(ii

1.	Solve the question:(i) x2 + xy + 8x + 8y(ii) 15xy − 6x + 5y − 2(iii) ax + bx − ay − by
Answer» (i) x²+ xy + 8x + 8y = x × x + x × y + 8 × x + 8 × y = x (x + y) + 8 (x + y) = (x + y) (x + 8) (ii) 15xy − 6x + 5y − 2 = 3 × 5 × x × y − 3 × 2 × x + 5 × y − 2 = 3x (5y − 2) + 1 (5y − 2) = (5y − 2) (3x + 1) (iii) ax + bx − ay − by = a × x + b × x − a × y − b × y = x (a + b) − y (a + b) = (a + b) (x − y)

Solve the question:(i) x2 + xy + 8x + 8y(ii) 15xy − 6x + 5y − 2(iii) ax + bx − ay − by

Answer»

(i) x²+ xy + 8x + 8y

= x × x + x × y + 8 × x + 8 × y

= x (x + y) + 8 (x + y)

= (x + y) (x + 8)

(ii) 15xy − 6x + 5y − 2

= 3 × 5 × x × y − 3 × 2 × x + 5 × y − 2

= 3x (5y − 2) + 1 (5y − 2)

= (5y − 2) (3x + 1)

(iii) ax + bx − ay − by

= a × x + b × x − a × y − b × y

= x (a + b) − y (a + b)

= (a + b) (x − y)