# Evaluate: (8x+3)^2

## Expression: ${\left( 8x+3 \right)}^{2}$

To expand the binomial, write it as a sum of products of coefficients of the expansion, the powers of $8x$ in descending order from $2$ to $0$ and the powers of $3$ in ascending order from $0$ to $2$

$? \times {\left( 8x \right)}^{2} \times {3}^{0}+? \times {\left( 8x \right)}^{1} \times {3}^{1}+? \times {\left( 8x \right)}^{0} \times {3}^{2}$

Substitute the coefficients from row ARG1 of Pascal's triangle, ARG2, into the expression

$1 \times {\left( 8x \right)}^{2} \times {3}^{0}+2 \times {\left( 8x \right)}^{1} \times {3}^{1}+1 \times {\left( 8x \right)}^{0} \times {3}^{2}$

Any expression multiplied by $1$ remains the same

${\left( 8x \right)}^{2} \times {3}^{0}+2 \times {\left( 8x \right)}^{1} \times {3}^{1}+1 \times {\left( 8x \right)}^{0} \times {3}^{2}$

Any expression multiplied by $1$ remains the same

${\left( 8x \right)}^{2} \times {3}^{0}+2 \times {\left( 8x \right)}^{1} \times {3}^{1}+{\left( 8x \right)}^{0} \times {3}^{2}$

To raise a product to a power, raise each factor to that power

$64{x}^{2} \times {3}^{0}+2 \times {\left( 8x \right)}^{1} \times {3}^{1}+{\left( 8x \right)}^{0} \times {3}^{2}$

Any non-zero expression raised to the power of $0$ equals $1$

$64{x}^{2} \times 1+2 \times {\left( 8x \right)}^{1} \times {3}^{1}+{\left( 8x \right)}^{0} \times {3}^{2}$

Any expression raised to the power of $1$ equals itself

$64{x}^{2} \times 1+2 \times 8x \times {3}^{1}+{\left( 8x \right)}^{0} \times {3}^{2}$

Any expression raised to the power of $1$ equals itself

$64{x}^{2} \times 1+2 \times 8x \times 3+{\left( 8x \right)}^{0} \times {3}^{2}$

Any non-zero expression raised to the power of $0$ equals $1$

$64{x}^{2} \times 1+2 \times 8x \times 3+1 \times {3}^{2}$

Any expression multiplied by $1$ remains the same

$64{x}^{2}+2 \times 8x \times 3+1 \times {3}^{2}$

Any expression multiplied by $1$ remains the same

$64{x}^{2}+2 \times 8x \times 3+{3}^{2}$

Calculate the product

$64{x}^{2}+48x+{3}^{2}$

Evaluate the power

$64{x}^{2}+48x+9$

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