Question

One of the factors of (1 + 3y)² + (9y² – 1) is
(a) 1 – 3y
(b) 3 – y
(c) 3y + 1
(d) y – 3

Answer 1

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One of the factors of (1 + 3y)² + (9y² – 1) is

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6y(3y+1)

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★$\huge\bf{\green{\underline{Explanation:-}}}$

• (1+3y)²+ (9y²-1)=
• (1+3y)²+ (3y+1)(3y-1)=
• (3y+1)(3y+1+3y-1)=
• (3y+1)6y= 6y(3y+1)

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Answer 2

One of the factors of (1 + 3y)² + (9y² – 1) is (3y + 1) (option c).

Given,

(1 + 3y)² + (9y² – 1)

To find,

The factors of (1 + 3y)² + (9y² – 1).

Solution,

The factors of (1 + 3y)² + (9y² – 1) are 6y (3y+1).

We can easily solve this problem by following the given steps.

Now,

(1 + 3y)² + (9y² – 1)

(1 + 3y)² + (3y + 1) (3y - 1) [ Factorising ( 9y² – 1) using the formula a²-b² = (a+b) (a-b). Here a is 3y and b is 1.]

(3y+1) (1+3y+3y-1) [Taking (3y+1) common]

(3y+1) 6y

Hence, the factors will be 6y(3y+1).

[Note that another way to find its factors is by solving (1+3y)² using the formula of (a+b)² = a²+b²+2ab. In this case, the value of a is 1 and the value of b is 3y.]