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Question
Factorize each of the following algebraic expression:
x2 − y2 − 4xz + 4z2
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Solution
\[x^2 - y^2 - 4xz + 4 z^2 \]
\[ = ( x^2 - 4xz + 4 z^2 ) - y^2 \]
\[ = [ x^2 - 2 \times x \times 2z + (2z )^2 ] - y^2 \]
\[ = (x - 2z )^2 - y^2 \]
\[ = [(x - 2z) - y][(x - 2z) + y]\]
\[ = (x - 2z - y)(x - 2z + y)\]
\[ = (x + y - 2z)(x - y - 2z)\]
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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 |
