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3. The equation [tex]a^2 = (b - x)^2 + h^2[/tex] is expanded to become [tex]a^2 = b^2 - 2bx + x^2 + h^2[/tex].

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To transform the equation [tex]\(a^2 = (b - x)^2 + h^2\)[/tex] into the form [tex]\(a^2 = b^2 - 2bx + x^2 + h^2\)[/tex], follow these algebraic steps:

1. Start with the original equation:
[tex]\[ a^2 = (b - x)^2 + h^2 \][/tex]

2. Expand the squared term [tex]\((b - x)^2\)[/tex] using the binomial expansion formula [tex]\((A - B)^2 = A^2 - 2AB + B^2\)[/tex]:
[tex]\[ (b - x)^2 = b^2 - 2bx + x^2 \][/tex]

3. Substitute this expanded form back into the original equation:
[tex]\[ a^2 = (b^2 - 2bx + x^2) + h^2 \][/tex]

4. Combine all the terms together:
[tex]\[ a^2 = b^2 - 2bx + x^2 + h^2 \][/tex]

Thus, the equation [tex]\(a^2 = (b-x)^2 + h^2\)[/tex] is expanded to become [tex]\(a^2 = b^2 - 2bx + x^2 + h^2\)[/tex].
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