Algebraic Identities

(x² - y²) × (x² + y²) = ______

• 2x² + 2y²
• x⁴ - y⁴
• x⁴ + y⁴
• 2x⁴

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

• x² - 64
• x² + 64
• x² - 16x + 64
• x² + 16x + 64

Add (a - b - c) ; (b - a - c) and (c - a - b)

• (a - b - c)
• (- a - b - c)
• (a + b - c)
• (-a - b + c)

What is the product of this monomial and polynomial ?
3xy ( 7z + 2z² + x + yx) 

• 21xyz + 3x²y + 6xy²z + 3x²y²
• 3x²y² + 6xyz² + 3xy² + 21xyz
• 6xy²z + 21xyz + 3xy² + 3x²y²
• 3x²y + 3x²y² + 6xyz² + 21xyz 

The length of a rectangle is decreased by 3 and breadth is increased by 4. The new area of the rectangle found after changing it's dimensions is same as that of original rectangle before any changes were made.
Which among below is a correct equation ?
Consider length of rectangle to be 'l' and breadth of rectangle to be 'b'

• 4l + 3b = 12
• 3l - 4b = 12
• 4l - 3b = 12
• 3l + 4b = 12

The simplified form of the expression (y² + 5)(y² - 3) is 

• y⁴ - 3y² - 15
• y⁴ + 2y² + 15
• y⁴ - 3y² + 15
• y⁴ + 2y² - 15

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

• x² + 4xy - 15xy
• 2x² + 4xy - 15xy
• x² - 15xy - 15xy
• 2x² - 6xy - 15xy

Simplify the following product (zx - y)(zx + k) using suitable identity.

• z²x² + (y - k)zx - ky
• z²x² + (k - y)zx - ky
• z²x² + (k - y)zx + ky
• z²x² + (y - k)zx + ky

If a + b = 5 and ab = 6, find a² + b².

• 13
• 12
• 10
• 11

Expand (4x − 5)(4x + 5).

• 4x² − 25

• 4x² + 25

• 16x² + 25

• 16x² − 25