Expand. If necessary, combine like terms. (2x+5)(2x-5)=

Recognize the pattern: Recognize the pattern in the expression (2x+5)(2x-5). This expression is in the form of (a+b)(a-b), which is a difference of squares. Special case: (a+b)(a-b) = a^2 - b^2Identify values of a and b: Identify the values of a and b. Compare (2x+5)(2x-5) with (a+b)(a-b). a = 2x b = 5Apply difference of squares formula: Apply the difference of squares formula to expand (2x+5)(2x-5). (a+b)(a-b) = a^2 - b^2 (2x+5)(2x-5) = (2x)^2 - (5)^2Simplify the expression: Simplify (2x)^2 - (5)^2. (2x)^2 - (5)^2 = (2x * 2x) - (5 * 5) = 4x^2 - 25

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Expand. If necessary, combine like terms.

(2x+5)(2x-5)=

Expand. If necessary, combine like terms. $\newline$ $(2x+5)(2x-5)=$

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Math Problems

Algebra 1

Multiply two binomials: special cases

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Q. Expand. If necessary, combine like terms.

\newline

(2x+5)(2x-5)=

Recognize the pattern: Recognize the pattern in the expression $(2x+5)(2x-5)$ . $\newline$ This expression is in the form of $(a+b)(a-b)$ , which is a difference of squares. $\newline$ Special case: $(a+b)(a-b) = a^2 - b^2$
Identify values of a and b: Identify the values of $a$ and $b$ . Compare $(2x+5)(2x-5)$ with $(a+b)(a-b)$ . $a = 2x$ $b = 5$
Apply difference of squares formula: Apply the difference of squares formula to expand $(2x+5)(2x-5)$ . $\newline$ $(a+b)(a-b) = a^2 - b^2$ $\newline$ $(2x+5)(2x-5) = (2x)^2 - (5)^2$
Simplify the expression: Simplify $(2x)^2 - (5)^2$ . $\newline$ $(2x)^2 - (5)^2 = (2x \cdot 2x) - (5 \cdot 5)$ $\newline$ $= 4x^2 - 25$