The product of this expression is option (A) (2√42 + 7√2 - 6 - √21) is the correct answer.
What is simplification of an expression?
Simplification of an expression is the process of writing an expression in the most efficient and compact form without affecting the value of the original expression. It involves, multiply out the brackets and then simplify the resulting expression by collecting the like terms.
For the given situation,
The expression is [tex](\sqrt{14} -\sqrt{3})( \sqrt{12} +\sqrt{7} )[/tex]
⇒ [tex]\sqrt{14}\sqrt{12} +\sqrt{14} \sqrt{7} -\sqrt{3} \sqrt{12} -\sqrt{3} \sqrt{7}[/tex]
⇒ [tex]\sqrt{168}+\sqrt{98}-\sqrt{36}-\sqrt{21}[/tex]
⇒ [tex]\sqrt{2^{2}(42) } +\sqrt{7^{2}(2) } -\sqrt{6^{2} }-\sqrt{21}[/tex]
⇒ [tex]2\sqrt{42 } +7\sqrt{2 } -6-\sqrt{21}[/tex]
Hence we conclude that the product of this expression is option (A) (2√42 + 7√2 - 6 - √21) is the correct answer.
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