1Cademy - Multiplying $$(4p - 7q)(4p + 7q)$$ Using the Product of Conjugates Pattern

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Multiplying $(5m - 9n)(5m + 9n)$ Using the Product of Conjugates Pattern

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Multiplying $(4p - 7q)(4p + 7q)$ Using the Product of Conjugates Pattern

Apply the Product of Conjugates Pattern to multiply $(4p - 7q)(4p + 7q)$ . Both binomials share the same first term $4p$ and the same last term $7q$ , with one using subtraction and the other addition, confirming they are conjugates. Use the formula $(a - b)(a + b) = a^2 - b^2$ , where $a = 4p$ and $b = 7q$ .

Step 1 — Square the first term, $4p$ : $(4p)^2 = 16p^2$ . Square the coefficient and the variable separately: $4^2 = 16$ and $p^2 = p^2$ . Step 2 — Square the last term, $7q$ : $(7q)^2 = 49q^2$ . Square both parts: $7^2 = 49$ and $q^2 = q^2$ . Step 3 — Write the difference of squares: $(4p - 7q)(4p + 7q) = 16p^2 - 49q^2$

The product is $16p^2 - 49q^2$ .

Updated 2026-05-25

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OpenStax Intermediate Algebra

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