Difference between revisions of "1963 AHSME Problems/Problem 21"
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\textbf{(E)}\ \text{the factor }x-y+z+1 </math> | \textbf{(E)}\ \text{the factor }x-y+z+1 </math> | ||
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Factor the perfect square trinomial. | Factor the perfect square trinomial. | ||
<cmath>x^2 - (y-z)^2 + x + y - z</cmath> | <cmath>x^2 - (y-z)^2 + x + y - z</cmath> | ||
Latest revision as of 13:43, 16 August 2021
Problem
The expression 
has:
Solution
Factor the perfect square trinomial.
![\[x^2 - (y-z)^2 + x + y - z\]](http://latex.artofproblemsolving.com/1/0/7/10722548328a889b191f586d439cc513f0e270fc.png)
Factor the difference of squares.
![\[(x+y-z)(x-y+z) + x + y - z\]](http://latex.artofproblemsolving.com/d/4/b/d4bd89edaa7c8243d439f5f22e3ed36c52d3eae7.png)
Factor by grouping.
![\[(x+y-z)(x-y+z+1)\]](http://latex.artofproblemsolving.com/6/b/c/6bc503fa83019ddfd2218f71dc4ba11d51a010eb.png)
The answer is 
.
See Also
| 1963 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 20 |
Followed by Problem 22 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
