We rewrite 97 as 100 – 3 and apply the subtraction square identity. Squaring 100 and 3, then subtracting twice their product gives the plain numerical solution.
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We express 27 as 30 – 3 and utilize the subtraction square identity. Squaring the terms and subtracting their double cross-product leaves the final calculation of 729.
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.
We split the middle term minus 11x into minus 15x plus 4x. Factoring by grouping yields the two expressions, filling the blanks with the number 3 and the term 5x.
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.