Question 182954
Do you want to factor?




{{{2x^2-98}}} Start with the given expression



{{{2(x^2-49)}}} Factor out the GCF {{{2}}}



Now let's focus on the inner expression {{{x^2-49}}}





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{{{x^2-49}}} Start with the given expression.



{{{(x)^2-49}}} Rewrite {{{x^2}}} as {{{(x)^2}}}.



{{{(x)^2-(7)^2}}} Rewrite {{{49}}} as {{{(7)^2}}}.



Notice how we have a difference of squares {{{A^2-B^2}}} where in this case {{{A=x}}} and {{{B=7}}}.



So let's use the difference of squares formula {{{A^2-B^2=(A+B)(A-B)}}} to factor the expression:



{{{A^2-B^2=(A+B)(A-B)}}} Start with the difference of squares formula.



{{{(x)^2-(7)^2=(x+7)(x-7)}}} Plug in {{{A=x}}} and {{{B=7}}}.



So this shows us that {{{x^2-49}}} factors to {{{(x+7)(x-7)}}}.



In other words {{{x^2-49=(x+7)(x-7)}}}.




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This means that {{{2(x^2-49)}}} factors further to {{{2(x+7)(x-7)}}}




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Answer:



So {{{2x^2-98}}} completely  factors to {{{2(x+7)(x-7)}}}