Question

СРОЧНО ПОМОГИТЕ!!! 10 БАЛЛОВ разложите на множители выражение 1. (p^3-q^2)(p^3+q^2) 2. (p^2-q)(p^2+q) 3. (m-n^3)(m+n^3) 4. (x^6+y^3)(x^6-y^3) 5. (-x^5+y^2)(y^2-x^5) 6. (p^7-q^6)(p^7+q^6)

Answer 1

$1)\; \; (p^3-q^2)(p^3+q^2)=(p^3)^2-(q^2)^2=p^6-q^4\\\\2)\; \; (p^2-q)(p^2+q)=(p^2)^2-q^2=p^4-q^2\\\\3)\; \; (m-n^3)(m+n^3)=m^2-(n^3)^2=m^2-n^6\\\\4)\; \; (x^6+y^3)(x^6-y^3)=(x^6)^2-(y^3)^2=x^{12}-y^6\\\\5)\; \; (-x^5+y^2)(y^2-x^5)=(y^2-x^5)^2=y^4-2y^2x^5+x^{10}\\\\5^*)\; \; (-x^5+y^2)(y^2+x^5)=(y^2)^2-(x^5)^2=y^4-x^{10}\\\\6)\; \; (p^7-q^6)(p^7+q^6)=(p^7)^2-(q^6)^2=p^{14}-q^{12}$

Answer 2

1. (p^3-q^2)(p^3+q^2) Using the difference of squares formula (a^2 - b^2) = (a + b)(a - b), we can rewrite the expression as: [(p^3)^2 - (q^2)^2] Now, we can apply the difference of squares formula: [(p^3 + q^2)(p^3 - q^2)]

2. (p^2-q)(p^2+q) Again, using the difference of squares formula, we have: [(p^2)^2 - (q)^2] Applying the difference of squares formula: [(p^2 + q)(p^2 - q)]

3. (m-n^3)(m+n^3) Using the difference of cubes formula (a^3 - b^3) = (a - b)(a^2 + ab + b^2), we can rewrite the expression as: [(m)^2 - (n^3)^2] Now, we can apply the difference of squares formula: [(m + n^3)(m - n^3)]

4. (x^6+y^3)(x^6-y^3) Applying the difference of cubes formula, we have: [(x^6)^2 - (y^3)^2] Using the difference of squares formula: [(x^6 + y^3)(x^6 - y^3)]

5. (-x^5+y^2)(y^2-x^5) Rearranging the terms, we have: (y^2 - x^5)(-x^5 + y^2) Now, we can apply the difference of squares formula: [(y^2)^2 - (x^5)^2] Using the difference of squares formula: [(y^2 + x^5)(y^2 - x^5)]

6. (p^7-q^6)(p^7+q^6) Applying the difference of squares formula, we have: [(p^7)^2 - (q^6)^2] Using the difference of squares formula: [(p^7 + q^6)(p^7 - q^6)]

In summary, the expressions can be factored as follows: 1. (p^3-q^2)(p^3+q^2) = (p^3 + q^2)(p^3 - q^2) 2. (p^2-q)(p^2+q) = (p^2 + q)(p^2 - q) 3. (m-n^3)(m+n^3) = (m + n^3)(m - n^3) 4. (x^6+y^3)(x^6-y^3) = (x^6 + y^3)(x^6 - y^3) 5. (-x^5+y^2)(y^2-x^5) = (y^2 + x^5)(y^2 - x^5) 6. (p^7-q^6)(p^7+q^6) = (p^7 + q^6)(p^7 - q^6)