Respuesta :
Answer:
see below
Step-by-step explanation:
The factoring of the difference of squares is ...
r² -s² = (r -s)(r +s)
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1) (1.2 -a^6b^6)(1.2+a^6b^6) . . . . . . . . r = 1.2, s = a^6b^6
2) (0.9p^3m^2 -0.1x)(0.9p^3m^2 +0.1x) . . . . . . . r = .9p^3m^2, s = 0.1x
Answer:
[tex]1.44 - a^{12} b^{12}=- \frac{1}{25} \left(5 a^{6} b^{6} - 6\right) \left(5 a^{6} b^{6} + 6\right)[/tex]
[tex]\frac{1}{100} {\left(81 m^{4} p^{6} - x^{2}\right)} = \frac{1}{100} {\left(9 m^{2} p^{3} - x\right) \left(9 m^{2} p^{3} + x\right)}[/tex]
Step-by-step explanation:
Factoring a polynomial involves writing it as a product of two or more polynomials. It reverses the process of polynomial multiplication.
Every polynomial that is a difference of squares can be factored by applying the following formula:
[tex]a^2-b^2=(a+b)(a-b)[/tex]
Note that a and b in the pattern can be any algebraic expression.
1. To express the polynomial [tex]1.44 - a^{12}b^{12}[/tex] in factored form you must:
- Convert the decimal number 1.44 to a fraction
Rewrite the decimal number as a fraction with 1 in the denominator
[tex]1.44 = \frac{1.44}{1}[/tex]
Multiply to remove 2 decimal places. Here, you multiply top and bottom by [tex]10^2 = 100[/tex]
[tex]\frac{1.44}{1}\times \frac{100}{100}= \frac{144}{100}[/tex]
Find the Greatest Common Factor (GCF) of 144 and 100, and reduce the fraction by dividing both numerator and denominator by GCF = 4
[tex]\frac{144 \div 4}{100 \div 4}= \frac{36}{25}[/tex]
[tex]1.44 - a^{12}b^{12}=\frac{36}{25} - a^{12} b^{12}[/tex]
- Factor the common term:
[tex]{\left(- a^{12} b^{12} + \frac{36}{25}\right)} = {\left(- \frac{1}{25} \left(25 a^{12} b^{12} - 36\right)\right)[/tex]
- Apply the difference of squares formula
[tex]- \frac{1}{25} {\left(25 a^{12} b^{12} - 36\right)} = - \frac{1}{25} {\left(5 a^{6} b^{6} - 6\right) \left(5 a^{6} b^{6} + 6\right)}[/tex]
2. To express the polynomial [tex]0.81p^6m^4-0.01x^2[/tex] in factored form you must:
- Convert the decimal numbers 0.81 and 0.01 to a fraction.
[tex]0.81=\frac{81}{100}[/tex]
[tex]0.01=\frac{1}{100}[/tex]
[tex]0.81p^6m^4-0.01x^2=\frac{81}{100} m^{4} p^{6} - \frac{x^{2}}{100}[/tex]
- Factor the common term:
[tex]{\left(\frac{81}{100} m^{4} p^{6} - \frac{x^{2}}{100}\right)} = {\left(\frac{1}{100} \left(81 m^{4} p^{6} - x^{2}\right)\right)}[/tex]
- Apply the difference of squares formula
[tex]\frac{1}{100} {\left(81 m^{4} p^{6} - x^{2}\right)} = \frac{1}{100} {\left(9 m^{2} p^{3} - x\right) \left(9 m^{2} p^{3} + x\right)}[/tex]
