Question
Use suitable identity to find the product:
$\left( {x + 4} \right)\left( {x + 10} \right)$
$\left( {x + 4} \right)\left( {x + 10} \right)$
✓
Answer
$\left( {x + 4} \right)\left( {x + 10} \right)$
We know that $\left( {x + a} \right)\left( {x + b} \right) = {x^2} + \left( {a + b} \right)x + ab$Here $a = 4$ and $b = 10$
We need to apply the above identity to find the product $\left( {x + 4} \right)\left( {x + 10} \right) = {x^2} + \left( {4 + 10} \right)x + \left( {4 \times 10} \right)$
$= {x^2} + 14x + 40.$
Therefore, we conclude that the product$ \left( {x + 4} \right)\left( {x + 10} \right)$ is ${x^2} + 14x + 40$
We know that $\left( {x + a} \right)\left( {x + b} \right) = {x^2} + \left( {a + b} \right)x + ab$Here $a = 4$ and $b = 10$
We need to apply the above identity to find the product $\left( {x + 4} \right)\left( {x + 10} \right) = {x^2} + \left( {4 + 10} \right)x + \left( {4 \times 10} \right)$
$= {x^2} + 14x + 40.$
Therefore, we conclude that the product$ \left( {x + 4} \right)\left( {x + 10} \right)$ is ${x^2} + 14x + 40$
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