Question

(ii) (12x2 - 6y2) (10x2 + 5y2) – (3x2 – 4y) ( x+y)

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Answer 1

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

(ii) ( 12x²-6y²)(10x²+5y²)-(3x²-4y)(x+y)

How to solve :

step by step explanation:

1. First we have to open the brackets and expanding the terms.
2. Now, rearranging the terms and make like terms together.
3. Simplify to simplest form and hence make it to factorise.
4. Factorise form or simplified form is your required answer.

=>12x²(10x²+5y²)-6y²(10x²+5y²)-(3x²-4y)(x+y)

Multiply with each and every term separately.

=>120x⁴+ 60x²y² -60x²y²-30y⁴-(3x²-4y)(x+y)

=>60x²y² -60x²y² will be cancelled as both are in opposite sign.

Concept:

[ If bases are same and in multiply then their power gets added]

eg.,=> aᵐ×aⁿ= aᵐ⁺ⁿ

Similarly in division only power gets substracted

e.g.,=>aᵐ ÷ aⁿ= aᵐ⁻ⁿ

=>120x⁴ -30 y⁴-[ (3x²(x+y)-4y(x+y)]

=>120x⁴-30y⁴-[3x³+3x²y -4xy -4y²]

Now, removing the brackets and expanding the term .

Note : When brackets will be remove the sign must be changed

=>120x⁴-30y⁴-3x³-3x²y+4xy+4y²

=> 30 ( 4x⁴-y⁴) -3x²( x+1) +4y( x+y) ( answer)

Answer 2

Question

(ii) ( 12x²-6y²)(10x²+5y²)-(3x²-4y)(x+y)

Required Answer -

1st

Let's see how to solve

How to solve :

step by step explanation:

First we have to open the brackets and expanding the terms.

Now, rearranging the terms and make like terms together.

Simplify to simplest form and hence make it to factorise.

Factorise form or simplified form is your required answer.

=>12x²(10x²+5y²)-6y²(10x²+5y²)-(3x²-4y)(x+y)

Multiply with each and every term separately.

=>120x⁴+ 60x²y² -60x²y²-30y⁴-(3x²-4y)(x+y)

=>60x²y² -60x²y² will be cancelled as both are in opposite sign.

Concept:

[ If bases are same and in multiply then their power gets added]

eg.,=> aᵐ×aⁿ= aᵐ⁺ⁿ

Similarly in division only power gets substracted

e.g.,=>aᵐ ÷ aⁿ= aᵐ⁻ⁿ

=>120x⁴ -30 y⁴-[ (3x²(x+y)-4y(x+y)]

=>120x⁴-30y⁴-[3x³+3x²y -4xy -4y²]

Now, removing the brackets and expanding the term .

Note : When brackets will be remove the sign must be changed

=>120x⁴-30y⁴-3x³-3x²y+4xy+4y²

=> 30 ( 4x⁴-y⁴) -3x²( x+1) +4y( x+y) ( answer)