Simplify the following expression:
49a
2
+70ab+25b
2
- A(7a+5b)
2 - B(7a−5b)
2 - C(5a−7b)
2 - D(5a+7b)
2
Solution & Step-by-step Explanation
The given expression is 49a
2
+70ab+25b
2
.
We can rewrite each term to check if it fits a standard algebraic identity:
49a
2
=(7a)
2
25b
2
=(5b)
2
70ab=2×(7a)×(5b)
Thus, the expression is in the form of x
2
+2xy+y
2
, which equals (x+y)
2
.
Where x=7a and y=5b.
Therefore:
49a
2
+70ab+25b
2
=(7a+5b)
2
2
+70ab+25b
2
.
We can rewrite each term to check if it fits a standard algebraic identity:
49a
2
=(7a)
2
25b
2
=(5b)
2
70ab=2×(7a)×(5b)
Thus, the expression is in the form of x
2
+2xy+y
2
, which equals (x+y)
2
.
Where x=7a and y=5b.
Therefore:
49a
2
+70ab+25b
2
=(7a+5b)
2