Question

1) (а²+2b)² 2) (x³+3y^{4})²

Answer 1

${a}^{4} + 4 {a}^{2} b + 4 {b}^{2}$
${x}^{6} + 6 {x}^{3} {y}^{4} + 9 {y}^{8}$

Answer 2

1) (а^2+2в)^2=(а^2)^2+2а^2×2в+(2в)^2=а^4+4а^2в+4в^2
2) (х^3+3у^4)^2=(х^3)^2+2х^3×3у^4+(3у^4)^2=х^6+6х^3у^4+9у^8

Answer 3

Sure, I can help you expand these expressions. To expand a square of a binomial, you can use the formula:

$$(a + b)^2 = a^2 + 2ab + b^2$$

Using this formula, let's expand the given expressions:

1. $(a^2 + 2b)^2$

Expanding this expression using the formula, we get:

$$(a^2 + 2b)^2 = a^4 + 2 \cdot a^2 \cdot 2b + (2b)^2 = a^4 + 4ab + 4b^2$$

2. $(x^3 + 3y^4)^2$

Using the same formula, expand this expression:

$$(x^3 + 3y^4)^2 = x^6 + 2 \cdot x^3 \cdot 3y^4 + (3y^4)^2 = x^6 + 6x^3y^4 + 9y^8$$

So, the expanded forms of the given expressions are:

1. $a^4 + 4ab + 4b^2$

2. $x^6 + 6x^3y^4 + 9y^8$