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gizmo_the_mogwai [7]
3 years ago
12

16(a+b)^2-49(a-b)^2 factorize the expression​

Mathematics
1 answer:
noname [10]3 years ago
4 0

The given expression is a difference of squares, so we have

16 (<em>a</em> + <em>b</em>)² - 49 (<em>a</em> - <em>b</em>)² = 4² (<em>a</em> + <em>b</em>)² - 7² (<em>a</em> - <em>b</em>)²

… = (4 (<em>a</em> + <em>b</em>))² - (7 (<em>a</em> - <em>b</em>))²

… = (4 (<em>a</em> + <em>b</em>) - 7 (<em>a</em> - <em>b</em>)) (4 (<em>a</em> + <em>b</em>) + 7 (<em>a</em> - <em>b</em>))

… = (4<em>a</em> + 4<em>b</em> - 7<em>a</em> + 7<em>b</em>) (4<em>a</em> + 4<em>b</em> + 7<em>a</em> - 7<em>b</em>)

… = (-3<em>a</em> + 11<em>b</em>) (11<em>a</em> - 3<em>b</em>)

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