Solve (160 + 2) ^ 2 = 106 ^ 2 * \{5(166 + 2 ^ 2) + 7(66 + 2 ^ 2) + 7 ^ 2\}

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Question

$$(160+2)^{2}=106^{2}\{5(166+2^{2})+7(66+2^{2})+7^{2}\}$$

Verify

$\text{false}$

Solution Steps

Add $160$ and $2$ to get $162$.

$$162^{2}=106^{2}\left(5\left(166+2^{2}\right)+7\left(66+2^{2}\right)+7^{2}\right)$$

Calculate $162$ to the power of $2$ and get $26244$.

$$26244=106^{2}\left(5\left(166+2^{2}\right)+7\left(66+2^{2}\right)+7^{2}\right)$$

Calculate $106$ to the power of $2$ and get $11236$.

$$26244=11236\left(5\left(166+2^{2}\right)+7\left(66+2^{2}\right)+7^{2}\right)$$

Calculate $2$ to the power of $2$ and get $4$.

$$26244=11236\left(5\left(166+4\right)+7\left(66+2^{2}\right)+7^{2}\right)$$

Add $166$ and $4$ to get $170$.

$$26244=11236\left(5\times 170+7\left(66+2^{2}\right)+7^{2}\right)$$

Multiply $5$ and $170$ to get $850$.

$$26244=11236\left(850+7\left(66+2^{2}\right)+7^{2}\right)$$

Calculate $2$ to the power of $2$ and get $4$.

$$26244=11236\left(850+7\left(66+4\right)+7^{2}\right)$$

Add $66$ and $4$ to get $70$.

$$26244=11236\left(850+7\times 70+7^{2}\right)$$

Multiply $7$ and $70$ to get $490$.

$$26244=11236\left(850+490+7^{2}\right)$$

Add $850$ and $490$ to get $1340$.

$$26244=11236\left(1340+7^{2}\right)$$

Calculate $7$ to the power of $2$ and get $49$.

$$26244=11236\left(1340+49\right)$$

Add $1340$ and $49$ to get $1389$.

$$26244=11236\times 1389$$

Multiply $11236$ and $1389$ to get $15606804$.

$$26244=15606804$$

Compare $26244$ and $15606804$.

$$\text{false}$$

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