Asked by Jamie Williams on Jul 06, 2024
Verified
Factor the perfect square trinomial 64a2−112a+4964 a ^ { 2 } - 112 a + 4964a2−112a+49 .
A) (8a+49) 2( 8 a + 49 ) ^ { 2 }(8a+49) 2
B) (8a−49) 2( 8 a - 49 ) ^ { 2 }(8a−49) 2
C) (8a−7) 2( 8 a - 7 ) ^ { 2 }(8a−7) 2
D) (64a+49) 2( 64 a + 49 ) ^ { 2 }(64a+49) 2
E) (8a+7) 2( 8 a + 7 ) ^ { 2 }(8a+7) 2
Perfect Square Trinomial
A trinomial that can be factored into two identical binomials, resulting from squaring a binomial.
- Determine the factors of perfect square trinomials.
Verified Answer
YA
Yasmin Avila
Jul 09, 2024
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) $(8a-7)^2$.
Learning Objectives
- Determine the factors of perfect square trinomials.