Question

8.
30c2 +19ac-63a2
6c-7a
9. (a6 + b) = (a + b2)
10. 6w + 7w2-12w+15
2w2 + 3w-5​

Answer 1

Answer:

$(1) 5 c+9 a \\(2) a^4-a^2 b^2+b^4 \\3) \frac{6 w^3+7 w^2-12 w+15}{(w-1)(2 w+5)}$

Step-by-step explanation:

Step:1 Rewrite the term: $30 c^2-35 a c+54 a c-63 a^2$

Regroup terms into two proportional parts : $\left(30 c^2-35 a c\right)+\left(54 a c-63 a^2\right)$Factor the expression: $5 c(6 c-7 a)+9 a(6 c-7 a)$

Factor the expression: (7 a-6 c)(-5 c-9 a)

Reduce the fraction: -(-5 c-9 a)

Remove the parentheses for addition or subtraction: 5 c+9 a

Answer: 5 c+9 a

Step:2 Rewrite as fraction: $\frac{a^6+b^6}{a^2+b^2}$

Factor the expression using $a^3 \pm b^3=(a \pm b)\left(a^2 \mp a b+b^2\right): \frac{\left(a^2+b^2\right)\left(\left(a^2\right)^2-a^2 b^2+\left(b^2\right)^2\right)}{a^2+b^2}$

Reduce the fraction: $\left(a^2\right)^2-a^2 b^2+\left(b^2\right)^2$

Simplify using exponent power rule $\left(a^n\right)^m=a^{n m}: a^4-a^2 b^2+b^4$

Answer: $a^4-a^2 b^2+b^4$

Step: 3Rewrite the term: $\frac{6 w^3+7 w^2-12 w+15}{2 w^2-2 w+5 w-5}$

Regroup terms into two proportional parts :$\frac{6 w^3+7 w^2-12 w+15}{\left(2 w^2-2 w\right)+(5 w-5)}$

Factor the expression: $\frac{6 w^3+7 w^2-12 w+15}{2 w(w-1)+5(w-1)}$

Factor the expression: $\frac{6 w^3+7 w^2-12 w+15}{(w-1)(2 w+5)}$

Answer: $\frac{6 w^3+7 w^2-12 w+15}{(w-1)(2 w+5)}$

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