# Which shows a difference of squares?

10y^{2}-4x^{2,}16y^{2}-x^{2,}8x^{2}-40x + 25, 64x^{2}-48x + 9

**Solution:**

The difference of two squares is a theorem that tells us if a quadratic equation can be written as a product of two binomials, in which one shows the difference of the square roots and the other shows the sum of the square roots.

We use the formula a^{2} - b^{2}= (a + b)(a - b)

If a term is possibly expressed in this form then the term is said to show the difference of squares.

**Case1:**

Consider 10y^{2} - 4x^{2}

Which can not be expressed in the form of a^{2}- b^{2}

Since 10 is not a perfect square.

**Case2:**

Consider 16y^{2} - x^{2}

Which can be expressed in the form of a^{2}- b^{2} as

16y^{2} - x^{2} =(4y + x)(4y - x)

**Case3:**

Consider 8x^{2} - 40x + 25

This polynomial cannot be factorized.

**Case-4**

Consider 64x^{2} - 48x + 9

This polynomial cannot be factorized.

## Which shows a difference of squares?

10y^{2}-4x^{2,}16y^{2}-x^{2,}8x^{2}-40x + 25, 64x^{2}-48x + 9

**Summary: **

The only term possible to express as perfect squares is 16y^{2} - x^{2}