Question

which polynomial can be simplified to a difference of squares? 10a2 3a – 3a – 16 16a2 – 4a 4a – 1 25a2 6a – 6a 36 24a2 – 9a 9a 4

Answer 1

For the polynomial: 10a^2 + 3a - 3a - 16 = 10a^2 - 16 but 10a^2 is not a perfect square hence does not simplify to a difference of two squares. For the polynomial: 16a^2 - 4a + 4a - 1 = 16a^2 - 1 = (4a - 1)(4a + 1). This polynomial simplifies to a difference of two squares. For 25a^2 + 6a - 6a + 36 = 25a^2 + 36. This ia a sum of two squares and not a difference of two squares. For 24a^2 - 9a + 9a + 4 = 24a^2 + 4. This ia a sum of two squares and not a difference of two squares.

Answer 2

The polynomial 16a² - 4a + 4a - 1 can be simplified to a difference of squares

What is a polynomial?

Polynomial is an expression that involves only the operations of addition, subtraction, multiplication of variables.

The difference of two squares is given by:

a² - b² = (a + b)(a - b)

Hence:

16a² - 4a + 4a - 1 = 4a(4a - 1) + 1(4a - 1)

= (4a + 1)(4a - 1)

The polynomial 16a² - 4a + 4a - 1 can be simplified to a difference of squares

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