Question

what is (ax+by)^2 + (bx-ay)^2?
Note:Factorise by grouping of terms.​

Answer 1

${(ax + by)^2+}$ ${(bx + ay)^2}$

This is your question, right? So, here is your answer.

• The terms are in "whole square" form, so what you need to do is -
• Multiply them twice, you get - ${a^2x^2 + b^2y^2+}$ ${b^2x^2 + a^2y^2}$
• Then group the terms with common factors, you get - ${a^2x^2 + a^2y^2+}$ ${b^2y^2 + b^2x^2}$
• Then pick out the common factor!
• So, you get - ${a^2 (x^2 + y^2)+}$ ${b^2 (x^2 + y^2)}$
• From this you get another common factor. What is that? Yes! ${x^2 + y^2}$
• So, your final answer will be - ${(x^2 + y^2)(a^2 + b^2)}$

Hope it helps you!!!