- 1) The factorization is: [tex]2a(a^2 + 2a + 4)[/tex]
- 2) The factorization is: [tex]6y^2(y - 7)(y + 7)[/tex]
- 3) The factorization is: [tex]5(x+5)^2[/tex]
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To factor each expression, we apply the given concepts, that is, greatest common factor, difference of squares and perfect squares.
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Expression 1:
The expression is:
[tex]2a^3 + 4a^2 + 8a[/tex]
First, we find the gcf of the numbers 2, 4 and 8, which is 2.
Of the exponents, the gcf between 3, 2 and 1 is 1, so:
[tex]2a^3 + 4a^2 + 8a = 2a(\frac{2a^3}{2a} + \frac{4a^2}{2a} + \frac{8a}{2a}) = 2a(a^2 + 2a + 4)[/tex]
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Expression 2:
The expression is:
[tex]6y^4 - 294y^2[/tex]
The gcf of 6 and 294 is 6.
The gcf of the exponents 2 and 4 is 4.
Thus:
[tex]6y^4 - 294y^2 = 6y^2(\frac{6y^4}{6y^2} - \frac{294y^2}{6y^2}) = 6y^2(y^2 - 49)[/tex]
Then, applying the difference of squares:
[tex]y^2 - 49 = (y - 7)(y + 7)[/tex]
Thus, the factored expression is:
[tex]6y^2(y^2 - 49) = 6y^2(y - 7)(y + 7)[/tex]
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Expression 3:
The expression is:
[tex]5x^2 + 50x + 125[/tex]
The gcf of the coefficients, 5, 50 and 125 is 5, so:
[tex]5(\frac{5x^2}{5} + \frac{50x}{5} + \frac{125}{5}) = 5(x^2 + 10x + 25)[/tex]
Applying the perfect square, we get that:
[tex]x^2 + 10x + 25 = (x + 5)^2[/tex]
Tus, the factored expression is:
[tex]5(x^2 + 10x + 25) = 5(x+5)^2[/tex]
A similar question is given at https://brainly.com/question/11930822
