We split 135 into 100 + 30 + 5 and expand it using the three-term identity. Summing the separate square values and their paired products provides the final answer.
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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 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.