Question

Упростите выражение(а+2ab)² - (a-b) (b+a) при а=1 и b=1/5

Answer 1

(а+2ab)² - (a-b) (b+a) =a²+4a²b+4a²b²-(a²-b²)=a²+4a²b+4a²b²-a²+b²=4a²b+4a²b²+b²=4*1²*1/5+4*1²(1/5)²+(1/5)²=4/5+4/25+1/25=4/5+1/5=1
при а=1 и b=1/5

Answer 2

A²+4a²b²+4a²b-(ab+a²-b²-ab)=a²+4a²b²+4a²b-ab-a²+b²+ab=b²+4a²b²+4a²b

Answer 3

I can help you with math problems. Here is the solution to your question:

To simplify the expression $(a+2ab)^2-(a-b)+(b+a)$, we can use the following steps:

- Expand the square term using the formula $(x+y)^2=x^2+2xy+y^2$. - Simplify the terms by combining like terms and applying the distributive property. - Substitute the values of $a$ and $b$ and evaluate the expression.

The detailed steps are shown below:

\begin{align*} (a+2ab)^2-(a-b)+(b+a) &= (a^2+4a^2b+4a^2b^2)-(a-b)+(b+a) && \text{expand the square term}\\ &= a^2+4a^2b+4a^2b^2-a+b+b+a && \text{simplify the terms}\\ &= 2a^2+4a^2b+4a^2b^2+2b && \text{combine like terms}\\ &= 2a(a+2ab)+2b(1+a) && \text{factor out common factors}\\ &= 2(1)(1+2(1)(1/5))+2(1/5)(1+1) && \text{substitute $a=1$ and $b=1/5$}\\ &= 2(1+2/5)+2(1/5)(2) && \text{simplify the fractions}\\ &= 2(7/5)+4/5 && \text{add the fractions}\\ &= 14/5+4/5 && \text{multiply the fractions}\\ &= 18/5 && \text{add the fractions} \end{align*}

Therefore, the simplified expression is $\frac{18}{5}$ or $3.6$. I hope this helps.Ответь+подробно.+Упростите+выражение(а+2ab)²+-+(a-b)+(b+a)+при+а=1+и+b=1/5