Question

(ax + by)^2 + ( ay - bx )^2 Factorise​

Answer 1

Required Answer:-

Given to factorise:

• (ax + by)² + (ay - bx)²

Solution:

(ax + by)² + (ay - bx)²

➡ Apply the formula, (a + b)² = a² + 2ab + b² and (a - b)² = a² - 2ab + b².

= a²x² + 2axby + b²y² + a²y² - 2axby + b²x²

Now, Simplify the result.

= a²x² + b²y² + a²y² + b²x²

Now, group each term,

= a²x² + a²y² + b²x² + b²y²

Now, take a² and b² as common,

= a²(x² + y²) + b²(x² + y²)

Again, take x² + y² as common,

= (x² + y²)(a² + b²)

Hence, we have found the result!!

Factorised form is (x² + y²)(a² + b²)

Note:- This question is factorised by grouping method.

Different Methods of factoring:

1. Factoring by taking out common factors.

2. Grouping method.

3. Splitting method. (middle term factorisation)

4. Factoring as difference of two squares and so on.

Answer 2

Answer:

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