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 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.
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 7x into 3x plus 4x. Factoring the expressions in pairs gives the two linear binomial factors which are (2x + 1) and (3x + 2).