Question

Factorise: 36y⁴-25y²+4​

Answer 1

Answer:

• Factorised form – (3y - 2)(3y + 2)(2y + 1)(2y - 1).

Solution:

Given To Factorise:

= 36y⁴ - 25y² + 4

We can rewrite it as:

= 36y⁴ - 24y² + 4 - y²

= (36y⁴ - 12y² - 12y² + 4) - y²

= {12y²(3y² - 1) - 4(3y² - 1)} - y²

= (12y² - 4)(3y² - 1) - y²

= 2(6y² - 2)(3y² - 1) - y²

= (6y² - 2)(6y² - 2) - y²

= (6y² - 2)² - y²

Using identity a² - b² = (a + b)(a - b), we get:

= (6y² + y - 2)(6y² - y - 2)

= {6y² - 3y + 4y - 2}{6y² - 4y + 3y - 2}

= {3y(2y - 1) + 2(2y - 1)}{2y(3y - 2) + 1(3y - 2)}

= (3y - 2)(2y + 1)(3y + 2)(2y - 1)

= (3y - 2)(3y + 2)(2y + 1)(2y - 1) (Answer)

Answer 2

STEP BY STEP EXPLANATION::::::----

STEP 1

Equation at the end of step 1

((36 • (y4)) - 52y2) + 4 = 0

STEP 2

Equation at the end of step

((22•32y4) - 52y2) + 4 = 0

STEP 3

To Factor by Splitting the Middle Term:::--

Factoring 36y4-25y2+4

The first term is, 36y4 its coefficient is 36 .

The middle term is, -25y2 its coefficient is -25 .

The last term, "the constant", is +4

Step-1 : Multiply the coefficient of the first term by the constant 36 • 4 = 144

Step-2 : Find two factors of 144 whose sum equals the coefficient of the middle term, which is -25 .

-144 + -1 = -145

-72 + -2 = -74

-48 + -3 = -51

-36 + -4 = -40

-24 + -6 = -30

-18 + -8 = -26

-16 + -9 = -25 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -16 and -9

36y4 - 16y2 - 9y2 - 4

Step-4 : Add up the first 2 terms, pulling out like factors :

4y2 • (9y2-4)

Add up the last 2 terms, pulling out common factors :

1 • (9y2-4)

Step-5 : Add up the four terms of step 4 :

(4y2-1) • (9y2-4)

Which is the desired factorization

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TO Factor as a Difference of Squares::--

Factoring: 4y2 - 1

Check : 4 is the square of 2

Check : 1 is the square of 1

Check : y2 is the square of y1

Factorization is : (2y + 1) • (2y - 1)

HENCE , FACTORIZED!!