Factor Theorem and Algebraic Identities

The expression (l + m) (2m + p) − 2m (p + m) can be simplified as

• 2lm + lp

• 2lm + lp − 2mp 

• 2lm + lp + mp 

• 2lm + lp − mp 

Find the product of (2x - 3y)(2x + 5y) using suitable identity.

• x² + 4xy - 15xy

• 2x² + 4xy - 15xy

• x² - 15xy - 15xy

• 2x² - 6xy - 15xy

The square of x² - 2y² is ______

• x⁴ - 4x²y² + 4y⁴

• x⁴ + 4x²y² + 4y⁴

• x⁴ - 4x²y² - 4y⁴

• None of the above

(x - 8) ( x - 8) = ______

• x² - 64

• x² + 64

• x² - 16x + 64

• x² + 16x + 64

(p - q)²

• p² + 2pq + q²

• p² + 2pq - q²

• p² - 2pq - q²

• p² - 2pq + q²

(5-p)(5-p) is of the form

• none of these

Expand (4x − 5)(4x + 5).

• 4x² − 25

• 4x² + 25

• 16x² + 25

• 16x² − 25

What is the product of (x² − y²) and (3x + 2y)?

• 3x³ − 2y³ + 3x²y + 3xy²

• 3x³ + 2y³ - 2x²y − 3xy²

• 3x³ − 2y³ + 2x²y − 3xy²

• 3x³ − 3y³ + 2x²y − 3xy²

The identity (y + a) (y +b) is

• y² + ( a - b )y + ab

• y² - ( a + b )y + ab

• y² + ( a + b )y - ab

• y² + ( a + b )y + ab