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 7x into 3x plus 4x. Factoring the expressions in pairs gives the two linear binomial factors which are (2x + 1) and (3x + 2).
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.
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).
We split the middle coefficient minus 11 into minus 3 and minus 8 because their sum equals minus 11 and their product equals positive 24. This gives the factors directly.