(a-6)(a+6)(36+а²)- (a²-18)² При а=-1/6

Вопрос школьника по предмету Математика

(a-6)(a+6)(36+а²)- (a²-18)²
При а=-1/6

Ответ учителя по предмету Математика

36{a}^{2}+{a}^{4}-1296-36{a}^{2}-{({a}^{2})}^{2}+2{a}^{2}times 18-{18}^{2}36a​2​​+a​4​​−1296−36a​2​​−(a​2​​)​2​​+2a​2​​×18−18​2​​

 {({x}^{a})}^{b}={x}^{ab}(x​a​​)​b​​=x​ab​​

36{a}^{2}+{a}^{4}-1296-36{a}^{2}-{a}^{4}+2{a}^{2}times 18-{18}^{2}36a​2​​+a​4​​−1296−36a​2​​−a​4​​+2a​2​​×18−18​2​​

Simplify {18}^{2}18​2​​ to 324324

36{a}^{2}+{a}^{4}-1296-36{a}^{2}-{a}^{4}+2{a}^{2}times 18-32436a​2​​+a​4​​−1296−36a​2​​−a​4​​+2a​2​​×18−324

Simplify 2{a}^{2}times 182a​2​​×18 to 36{a}^{2}36a​2​​

36{a}^{2}+{a}^{4}-1296-36{a}^{2}-{a}^{4}+36{a}^{2}-32436a​2​​+a​4​​−1296−36a​2​​−a​4​​+36a​2​​−324

 Collect like terms

(36{a}^{2}-36{a}^{2}+36{a}^{2})+({a}^{4}-{a}^{4})-1296-324(36a​2​​−36a​2​​+36a​2​​)+(a​4​​−a​4​​)−1296−324

Simplify

36{a}^{2}-1296-32436a​2​​−1296−324

 

Simplify

36{a}^{2}-162036a​2​​−1620