Question

$(2g+ 3h)x^{3}$

Answer 1

$(2g+3h)x^{3}=2gx^{3}+3hx^{3}$

Step-by-step explanation:

Now, $(2g+3h)x^{3}$

• Simply use the formula $(a+b)c=ab+ac$ to find the expanded form of the given expression.

• Then calculate the terms to find its simplified form.

$=2g\times x^{3}+3h\times x^{3}$

$=2hx^{3}+3hx^{3}$

If we consider the question to be $(2g+3h)^{3}$:

Now, $(2g+3h)^{3}$

$=(2g)^{3}+3\times (2g)^{2}\times 3h+3\times 2g\times (3h)^{2}+(3h)^{3}$

• We use the algebraic formula,

• $(a+b)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3}$

$=8g^{3}+3\times 4g^{2}\times 3h+3\times 2g\times 9h^{2}+27h^{3}$

$=8g^{3}+36g^{2}h+54gh^{2}+27h^{3}$

Answer 2

Given:

(2g + 3h)x³

To Find:

The simplification of the given equation

Solution:

We multiply the given equation with x³ which will be equal to 2gx³ + 3hx³

Then, we simplify the given formula by using the formula (a + b)c = ab + ac to find the expanded form of the given equation. Then, we calculate the terms of the equation to find the simplification

⇒ 2g × x³ + 3h × x³

⇒ 2h³ + 3hx³

Let the equation be (2g + 3h)³

By using the algebraic formula

(a + b)³ = a³ + 3a²b + 3ab² + b³

put the equation in the algebraic formula

Now, (2g)³ + 3 × (2g)² × 3h + 3 × 2g × (3h)² + (3h)³

We now simplify the equation

⇒ 8g³ + 3 × 4g² × 3h + 3 × 2g × 9h² + 27h³

⇒ 8g³ + 36g²h + 54gh² + 27h³

Therefore the given equation is simplified.