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Question
Factorize each of the following algebraic expression:
x2 − y2 + 6y − 9
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Solution
\[x^2 - y^2 + 6y - 9\]
\[ = x^2 - ( y^2 - 6y + 9)\]
\[ = x^2 - ( y^2 - 2 \times y \times 3 + 3^2 )\]
\[ = x^2 - (y - 3 )^2 \]
\[ = [x - (y - 3)][x + (y - 3)]\]
\[ = (x - y + 3)(x + y - 3)\]
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Match the following :
| Column A | Column B |
| (a) `x/2` = 10 | (i) x = 4 |
| (b) 20 = 6x − 4 | (ii) x = 1 |
| (c) 2x − 5 = 3 − x | (iii) x = 20 |
| (d) 7x − 4 − 8x = 20 | (iv) x = `8/3` |
| (e) `4/11 - x = (-7)/11` | (v) x = −24 |
