Question

1. 3a^2+12a+12/3a+6 2. 8a^2-16a+8/2a-2

Answer 1

1). 3*(a^2+4a+4) / 3(a+2)=3*(a+2)^2 / 3*(a+2)=a+2. 2). 8*(a^2-2a+1) / 2*(a-1)=8*(a-1)^2 / 2*(a-1)=4*(a-1)=4a-4.

Answer 2

To simplify the given expressions, we'll start by factoring the numerators and denominators and then canceling out common factors:

1. Expression: (3a^2 + 12a + 12) / (3a + 6)

Step 1: Factor the numerator Numerator: 3a^2 + 12a + 12 Common factor in the numerator is 3, so we can factor it out: Numerator = 3(a^2 + 4a + 4)

Step 2: Factor the denominator Denominator: 3a + 6 Common factor in the denominator is 3, so we can factor it out: Denominator = 3(a + 2)

Now the expression becomes: (3(a^2 + 4a + 4)) / (3(a + 2))

Step 3: Cancel out the common factor (3) in the numerator and denominator: Result: (a^2 + 4a + 4) / (a + 2)

2. Expression: (8a^2 - 16a + 8) / (2a - 2)

Step 1: Factor the numerator Numerator: 8a^2 - 16a + 8 Common factor in the numerator is 8, so we can factor it out: Numerator = 8(a^2 - 2a + 1)

Step 2: Factor the denominator Denominator: 2a - 2 Common factor in the denominator is 2, so we can factor it out: Denominator = 2(a - 1)

Now the expression becomes: (8(a^2 - 2a + 1)) / (2(a - 1))

Step 3: Cancel out the common factor (2) in the numerator and denominator: Result: (4(a^2 - 2a + 1)) / (a - 1)

Final results:

1. Simplified form: (a^2 + 4a + 4) / (a + 2)

2. Simplified form: (4(a^2 - 2a + 1)) / (a - 1)

If you need further simplification, you can try factoring the numerators completely or expanding the squared terms.