We change 41 into 40 + 1 and apply the addition square identity. Squaring 40 and 1, then adding twice their product gives the plain numerical solution.
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We split the middle term minus 4x into minus 7x plus 3x to factor the expression by grouping. Taking out common factors leaves (3x – 7) multiplied by (x + 1).
Expanding the left side yields 3a square + 3b square + 3c square – 2ab – 2bc – 2ca, which does not match the right side. Therefore, the given mathematical equation is false.
This six-term polynomial matches the expanded three-term identity. The squared bases are m/3, k/2, and 3n, which merge into the single grouped factor (m/3 + k/2 + 3n) square.
This fits the identity a square + 2ab + b square. The first term is the square of 3/2 s and the last is the square of 2t, which yields the factor (3/2 s + 2t) square.