Difference of two squaresA number in front of x²
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Each one is a difference of two squares. Factor it.
19x² − 25
29x² − 784
381x² − 625
425x² − 1156
536x² − 625
625x² − 49
749x² − 225
816x² − 81
99x² − 4
1064x² − 49
Difference of squares with coefficients worksheets
9x² − 64 is still one square minus another — but now the square in front matters. These free printable worksheets factor a difference of squares that carries a coefficient on x².
If they get stuck
Difference of squares with coefficients
The answer key prints on a separate page.
What's on this sheet
The pattern is the same as the plain case, sum times difference, but the root a child takes is the harder one. √(9x²) is 3x — not 9x, and not 3 — because it is the root of the number and the root of x² taken together. That single step is what this sheet exists to drill, and it is the one students skip.
Why this sheet works
So 9x² − 64 factors as (3x + 8)(3x − 8), and checking it means multiplying back out until the middle terms cancel. Seeing +24x and −24x disappear is the whole proof that there is no middle term, and it also catches the child who wrote 9x by mistake, because then the outer and inner products would not cancel.
How this one works
One question from a sheet like this one, worked a step at a time — with a sentence saying what just happened and why.
Difference of squares with coefficients, step by step