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].
