Video narration
Can you square 47 without doing the whole long-multiplication problem? Yes-use the same carrying you know from columns. The digits make three pieces: square the right digit, double the digits multiplied together, then square the left digit. This pattern is called "Vertically and Crosswise": square each digit, then multiply the two across and double. Now carry it from right to left. Seven squared is 49: write 9 in the ones place and carry 4. For the middle, double 4 times 7: that's 56. Add the carried 4, making 60; write 0 in the next place and carry 6. Finally, 4 squared is 16. Add the 6 you carried, giving 22. Read the digits in place: 2209. So, can you do 47 squared without long multiplication? Yes: square the last digit, double the cross-product, square the first, and carry right to left.