Factor the perfect square trinomial 64 a ^ { 2 } - 112 a + 49 . A) ( 8 a + 49 ) ^ { 2 } B) ( 8 a - 49 ) ^ { 2 } C) ( 8 a - 7 ) ^ { 2 } D) ( 64 a + 49 ) ^ { 2 } E) ( 8 a + 7 ) ^ { 2 }

Question

Factor the perfect square trinomial  64 a ^ { 2 } - 112 a + 49  . A)  ( 8 a + 49 ) ^ { 2 }  B)  ( 8 a - 49 ) ^ { 2 }  C)  ( 8 a - 7 ) ^ { 2 }  D)  ( 64 a + 49 ) ^ { 2 }  E)  ( 8 a + 7 ) ^ { 2 }

Yasmin Avila · Accepted Answer

Final Answer : C, Explanation :  To factor a perfect square trinomial of the form $a^2-2ab+b^2$, we can use the pattern $(a-b)^2=a^2-2ab+b^2$. Here, we have $64a^2-112a+49$, which can be rewritten as $(8a)^2-2(8a)(7)+7^2$. Using the pattern, this equals $(8a-7)^2$. Therefore, the answer is (C) $(8a-7)^2$.

Factor the perfect square trinomial $64 a ^ { 2 } - 112 a + 49$ .

A) $8 a + 49 ) ^ { 2 }$
B) $8 a - 49 ) ^ { 2 }$
C) $8 a - 7 ) ^ { 2 }$
D) $64 a + 49 ) ^ { 2 }$
E) $8 a + 7 ) ^ { 2 }$

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