Question

FACTORISE:-12(X-2Y)^2-(X-2Y)-35​

Answer 1

Answer:

Step by Step Solution

Step by Step SolutionMore Icon

Step by Step SolutionMore IconSTEP

Step by Step SolutionMore IconSTEP1

Step by Step SolutionMore IconSTEP1:

Step by Step SolutionMore IconSTEP1:Equation at the end of step 1

Step by Step SolutionMore IconSTEP1:Equation at the end of step 1 (12 • (x - 2y)2 - (x - 2y)) - 35

Step by Step SolutionMore IconSTEP1:Equation at the end of step 1 (12 • (x - 2y)2 - (x - 2y)) - 35 STEP

Step by Step SolutionMore IconSTEP1:Equation at the end of step 1 (12 • (x - 2y)2 - (x - 2y)) - 35 STEP 2

Step by Step SolutionMore IconSTEP1:Equation at the end of step 1 (12 • (x - 2y)2 - (x - 2y)) - 35 STEP 2 :

Step by Step SolutionMore IconSTEP1:Equation at the end of step 1 (12 • (x - 2y)2 - (x - 2y)) - 35 STEP 2 :Trying to factor by pulling out :

Step by Step SolutionMore IconSTEP1:Equation at the end of step 1 (12 • (x - 2y)2 - (x - 2y)) - 35 STEP 2 :Trying to factor by pulling out : 2.1 Factoring: 12x2-48xy-x+48y2+2y-35

Step by Step SolutionMore IconSTEP1:Equation at the end of step 1 (12 • (x - 2y)2 - (x - 2y)) - 35 STEP 2 :Trying to factor by pulling out : 2.1 Factoring: 12x2-48xy-x+48y2+2y-35 Thoughtfully split the expression at hand into groups, each group having two terms

Looking for common sub-expressions :

Looking for common sub-expressions : Group 1: (12x-1) • (x)

Looking for common sub-expressions : Group 1: (12x-1) • (x)Group 3: (2y-35) • (1)

Looking for common sub-expressions : Group 1: (12x-1) • (x)Group 3: (2y-35) • (1)Group 2: (x-y) • (-48y)

Looking for common sub-expressions : Group 1: (12x-1) • (x)Group 3: (2y-35) • (1)Group 2: (x-y) • (-48y)Bad news !! Factoring by pulling out fails :

Looking for common sub-expressions : Group 1: (12x-1) • (x)Group 3: (2y-35) • (1)Group 2: (x-y) • (-48y)Bad news !! Factoring by pulling out fails : The groups have no common factor and can not be added up to form a multiplication.

Looking for common sub-expressions : Group 1: (12x-1) • (x)Group 3: (2y-35) • (1)Group 2: (x-y) • (-48y)Bad news !! Factoring by pulling out fails : The groups have no common factor and can not be added up to form a multiplication.Final result :

Looking for common sub-expressions : Group 1: (12x-1) • (x)Group 3: (2y-35) • (1)Group 2: (x-y) • (-48y)Bad news !! Factoring by pulling out fails : The groups have no common factor and can not be added up to form a multiplication.Final result : 12x2 - 48xy - x + 48y2 + 2y - 35

Answer 2

Answer:

12(x-2y)^2 - (x-2y) - 35

Let (x-2y) = a

Therefore,

12a^2 - a - 35

= 12a^2 - (21a - 20a) - 35

= 12a^2 - 21a + 20a - 35

= 3a(4a - 7) + 5(4a - 7)

= (4a - 7) (3a + 5)

put (a = x-2y)

= {4(x-2y)-7} {3(x-2y)+5}

= (4x - 8y - 7) (3x - 6y + 5)

Answer :- (4x - 8y - 7) (3x - 6y + 5)

Rough portion,

Note :- First,

35×12 = 420

second,

prime factors of 420 = 2×2×3×5×7×1

Third,

(3×7×1) - (2×2×5)

= 21 - 20

= 1