Question

1. factor $81x^2 - 180x + 100$ using the perfect square trinomial method of factoring.a. $(9x - 10)(9x - 10)$b. $(9x - 10)^2$c. $(9x + 10)^2$d. it is not a perfect square trinomial2. factor $81b^2 + b + 1$ using the perfect square trinomial method of factoring.a. it is not a perfect square trinomialb. $(9b + 1)^2$c. $(9b - 1)^2$d. $(9b + 1)(9b - 20)$3. factor $100a^2 + 116a + 108$ using the perfect square trinomial method of factoring.a. $(10a + 3)^2$b. it is not a perfect square trinomialc. $(10a + 54)^2$d. $(10a - 10)^2$4. factor $49b^2 + 280b + 400$ using the perfect square trinomial method of factoring.a. $(7b + 20)^2$b. $(7b - 20)^2$c. it is not a perfect square trinomiald. $(7b + 40)^2$5. factor $16b^2 - 12b - 18$ using the perfect square trinomial method of factoring.a. $(4b - 3)(4b - 12)$b. $(4b - 3)^2$c. it is not a perfect square trinomiald. $(4b - 5)^2$6. factor $36a^2 + 84a + 49$ using the perfect square trinomial method of factoring.a. $(6a + 7)^2$b. $(6a - 7)^2$c. $(6a + 7)(6a - 7)$d. it is not a perfect square trinomial

Explanation:

Step1: Identify perfect square trinomial

A perfect square trinomial follows $a^2+2ab+b^2=(a+b)^2$ or $a^2-2ab+b^2=(a-b)^2$.
For $81x^2+180x+100$: $81x^2=(9x)^2$, $100=10^2$, $2*9x*10=180x$.
Expression: $81x^2+180x+100=(9x+10)^2$

Step2: Match with options

Option A is $(9x+10)^2$, which matches.

Step1: Identify perfect square trinomial

For $16t^2-8t+1$: $16t^2=(4t)^2$, $1=1^2$, $2*4t*1=8t$ (matches the middle term sign).
Expression: $16t^2-8t+1=(4t-1)^2$

Step2: Match with options

Option B is $(4t - 1)^2$, which matches.

Step1: Identify perfect square trinomial

For $9b^2+114b+361$: $9b^2=(3b)^2$, $361=19^2$, $2*3b*19=114b$.
Expression: $9b^2+114b+361=(3b+19)^2$

Step2: Match with options

Option A is $(3b + 19)^2$, which matches.

Step1: Identify perfect square trinomial

For $49p^2-196p+196$: $49p^2=(7p)^2$, $196=14^2$, $2*7p*14=196p$ (matches the middle term sign).
Expression: $49p^2-196p+196=(7p-14)^2$

Step2: Match with options

Option B is $(7p - 14)^2$, which matches.

Answer:

A. $(9x + 10)^2$

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