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Question

solve: $$ab\left( {{x^2} + 1} \right) + x\left( {{a^2} + {b^2}} \right)$$


Solution

$$ab\left( { x }^{ 2 }+1 \right) +x\left( a^2+b^2 \right) $$
$$\Rightarrow abx^2+ab+xa^2+xb^2$$
      $$abx^2+a^2x+bx^2+ab$$
      $$ax\left( xb+a \right) +b\left( bx+a \right) $$
      $$\left( ax+b \right) \left( xb+a \right).$$
Hence, the answer is $$\left( ax+b \right) \left( xb+a \right).$$

Mathematics

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