Question

(y² + 2y + 3) × (y² + 2 y - 3)​

Answer 1

Answer:

y⁴ + 4y³ + 4y² - 9

Step-by-step explanation:

(y² + 2y + 3) × (y² + 2 y - 3)​

= y²(y² + 2 y - 3)​  + 2y (y² + 2 y - 3)​ + 3 (y² + 2 y - 3)​

= y⁴ + 2y³ - 3y² + 2y³ + 4y² - 6y + 3y² + 6y - 9

= y⁴ + 4y³ + 4y² - 9

Answer 2

Answer:

Factorise the given equation 2y3 + y2 - 2y - 1

Answer:

A polynomial is an algebraic expression in which the exponent on any variable is a whole number. Polynomial’s degree is the highest or the greatest power of a variable in a polynomial equation.

A polynomial can be written as the product of its factors having a degree less than or equal to the original polynomial.

The process of factoring is called factorization of polynomials.

Given that 2y³ + y² – 2y – 1

Now Factorizing

2y³ + y² – 2y – 1

= y² (2y + 1) -1 (2y + 1)

= (2y + 1)(y² – 1)

= (2y + 1)(y² – 1²)

By algebraic identity:

a² – b² = (a + b) (a – b)

(y² – 1²) = (y + 1)(y – 1)

(y² – 1²) can be written as (y + 1) (y – 1)

∴ (2y + 1)(y² – 1²)= (2y + 1) (y + 1) (y – 1)

Therefore,

2y³ + y² – 2y – 1 = (2y + 1) (y + 1) (y-1)

Check the video for more details on the factorisation of algebraic expression