Solved on Feb 07, 2024

Expand the expression $(a-5)^{2}$ and write the result in standard form.

STEP 1

Assumptions
1. We need to expand the expression $(a-5)^2$ .
2. Standard form means writing the expression as a polynomial in descending powers of $a$ .

STEP 2

Recognize that $(a-5)^2$ is the square of a binomial.
$(a-5)^2 = (a-5)(a-5)$

STEP 3

Use the FOIL (First, Outer, Inner, Last) method to expand the product of two binomials.
$(a-5)(a-5) = a \cdot a + a \cdot (-5) + (-5) \cdot a + (-5) \cdot (-5)$

STEP 4

Multiply the terms using the distributive property.
$a \cdot a = a^2$ $a \cdot (-5) = -5a$ $(-5) \cdot a = -5a$ $(-5) \cdot (-5) = 25$

STEP 5

Combine the terms to write the expression in standard form.
$a^2 - 5a - 5a + 25$

STEP 6

Combine like terms.
$a^2 - 10a + 25$
The expression in standard form is $a^2 - 10a + 25$ .

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Expand the expression $(a-5)^{2}$ and write the result in standard form.

STEP 1

Assumptions
1. We need to expand the expression $(a-5)^2$ .
2. Standard form means writing the expression as a polynomial in descending powers of $a$ .

STEP 2

Recognize that $(a-5)^2$ is the square of a binomial.
$(a-5)^2 = (a-5)(a-5)$

STEP 3

Use the FOIL (First, Outer, Inner, Last) method to expand the product of two binomials.
$(a-5)(a-5) = a \cdot a + a \cdot (-5) + (-5) \cdot a + (-5) \cdot (-5)$

STEP 4

Multiply the terms using the distributive property.
$a \cdot a = a^2$ $a \cdot (-5) = -5a$ $(-5) \cdot a = -5a$ $(-5) \cdot (-5) = 25$

STEP 5

Combine the terms to write the expression in standard form.
$a^2 - 5a - 5a + 25$

STEP 6

Combine like terms.
$a^2 - 10a + 25$
The expression in standard form is $a^2 - 10a + 25$ .

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Expand the expression (a−5)2(a-5)^{2}(a−5)2 and write the result in standard form.

STEP 1

Assumptions1. We need to expand the expression (a−5)2(a-5)^2(a−5)2.2. Standard form means writing the expression as a polynomial in descending powers of aaa.

STEP 2

Recognize that (a−5)2(a-5)^2(a−5)2 is the square of a binomial.(a−5)2=(a−5)(a−5) (a-5)^2 = (a-5)(a-5) (a−5)2=(a−5)(a−5)

STEP 3

Use the FOIL (First, Outer, Inner, Last) method to expand the product of two binomials.(a−5)(a−5)=a⋅a+a⋅(−5)+(−5)⋅a+(−5)⋅(−5) (a-5)(a-5) = a \cdot a + a \cdot (-5) + (-5) \cdot a + (-5) \cdot (-5) (a−5)(a−5)=a⋅a+a⋅(−5)+(−5)⋅a+(−5)⋅(−5)

STEP 4

Multiply the terms using the distributive property.a⋅a=a2 a \cdot a = a^2 a⋅a=a2 a⋅(−5)=−5a a \cdot (-5) = -5a a⋅(−5)=−5a (−5)⋅a=−5a (-5) \cdot a = -5a (−5)⋅a=−5a (−5)⋅(−5)=25 (-5) \cdot (-5) = 25 (−5)⋅(−5)=25

STEP 5

Combine the terms to write the expression in standard form.a2−5a−5a+25 a^2 - 5a - 5a + 25 a2−5a−5a+25

STEP 6

Combine like terms.a2−10a+25 a^2 - 10a + 25 a2−10a+25The expression in standard form is a2−10a+25a^2 - 10a + 25a2−10a+25.

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Expand the expression $(a-5)^{2}$ and write the result in standard form.

Assumptions
1. We need to expand the expression $(a-5)^2$ .
2. Standard form means writing the expression as a polynomial in descending powers of $a$ .

Recognize that $(a-5)^2$ is the square of a binomial.
$(a-5)^2 = (a-5)(a-5)$

Use the FOIL (First, Outer, Inner, Last) method to expand the product of two binomials.
$(a-5)(a-5) = a \cdot a + a \cdot (-5) + (-5) \cdot a + (-5) \cdot (-5)$

Multiply the terms using the distributive property.
$a \cdot a = a^2$ $a \cdot (-5) = -5a$ $(-5) \cdot a = -5a$ $(-5) \cdot (-5) = 25$

Combine the terms to write the expression in standard form.
$a^2 - 5a - 5a + 25$

Combine like terms.
$a^2 - 10a + 25$
The expression in standard form is $a^2 - 10a + 25$ .