x²a + x²b – 16a – 16b
(x²a + x²b) – (16a – 16b)
x² (a + b) – 16 (a + b)
(x² – 16)(a + b)²
(x + 4)(x – 4)(a + b)²
For factoring the x² (a + b) – 16 (a + b), would the answer be ( x²-16) (a+b)²? and not ( x²-16) (a+b)? why or why not?
(x²a + x²b) – (16a – 16b)
x² (a + b) – 16 (a + b)
(x² – 16)(a + b)²
(x + 4)(x – 4)(a + b)²
For factoring the x² (a + b) – 16 (a + b), would the answer be ( x²-16) (a+b)²? and not ( x²-16) (a+b)? why or why not?
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Answer:
The correct factorization of x²(a + b) - 16(a + b) is (x² - 16)(a + b) because we need to factor out the common factor of (a + b) from both terms before further simplifying.
If we factor out (a + b) from the expression, we get:
x²(a + b) - 16(a + b) = (a + b)(x² - 16)
Now, we can further simplify (x² - 16) by factoring it as the difference of two squares:
(x² - 16) = (x + 4)(x - 4)
Therefore, the final factorization of x²(a + b) - 16(a + b) is:
(x + 4)(x - 4)(a + b)