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Let's solve the equation. First, we'll simplify the algebraic expressions using the perfect square binomial formula:
We'll apply this formula and expand the parentheses in the expressions in the equation:
We'll continue and combine like terms, by moving terms between sides. Then we can notice that the squared term cancels out, therefore it's a first-degree equation, which we'll solve by isolating the variable term on one side and dividing both sides of the equation by its coefficient:
Therefore, the correct answer is answer A.
Declares the given expression as a sum
\( (7b-3x)^2 \)
Taking square roots would give you , which creates two cases. But this approach misses the algebraic structure. Expanding first reveals the linear relationship more clearly.
When both sides have the same squared expression (like here), they'll cancel during simplification. This transforms a quadratic-looking equation into a simpler linear one!
If you had , the constants wouldn't cancel. You'd still expand both sides, but you'd get a different linear equation to solve.
Generally no! After expanding and simplifying, you usually get a linear equation with exactly one solution, like giving .
Think of FOIL: First, Outer, Inner, Last terms. For , you get . The middle term is always !
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