Question

выполните умножение: а)(y-3)(y+3) б)(1-x)(1+x) в)(m-n)(m+n) г)(x+y)(x-y) д)(x-2)(2+x) е)(c+a)(a-c)

Answer 1

а) (y-3)(y+3)

To multiply these two binomials, we can use the distributive property. We multiply each term in the first binomial by each term in the second binomial and then combine like terms, if any.

Let's start by multiplying the first terms of each binomial: y * y = y^2

Next, let's multiply the outer terms: y * 3 = 3y

Then, let's multiply the inner terms: -3 * y = -3y

Finally, let's multiply the last terms: -3 * 3 = -9

Now, let's combine the like terms: y^2 + 3y - 3y - 9

The 3y and -3y cancel each other out, so we are left with: y^2 - 9

Therefore, the product of (y-3)(y+3) is y^2 - 9.

б) (1-x)(1+x)

Using the same process as above, let's multiply these two binomials:

First terms: 1 * 1 = 1

Outer terms: 1 * x = x

Inner terms: -1 * 1 = -1

Last terms: -1 * x = -x

Combining the like terms: 1 + x - 1 - x

The x and -x cancel each other out, so we are left with: 1 - 1

The result is 0.

в) (m-n)(m+n)

Again, let's multiply these two binomials:

First terms: m * m = m^2

Outer terms: m * n = mn

Inner terms: -n * m = -mn

Last terms: -n * n = -n^2

Combining the like terms: m^2 + mn - mn - n^2

The mn and -mn cancel each other out, so we are left with: m^2 - n^2

Therefore, the product of (m-n)(m+n) is m^2 - n^2.

г) (x+y)(x-y)

Let's multiply these two binomials:

First terms: x * x = x^2

Outer terms: x * -y = -xy

Inner terms: y * x = xy

Last terms: y * -y = -y^2

Combining the like terms: x^2 - xy + xy - y^2

The xy and -xy cancel each other out, so we are left with: x^2 - y^2

Hence, the product of (x+y)(x-y) is x^2 - y^2.

д) (x-2)(2+x)

Let's multiply these two binomials:

First terms: x * 2 = 2x

Outer terms: x * x = x^2

Inner terms: -2 * 2 = -4

Last terms: -2 * x = -2x

Combining the like terms: 2x + x^2 - 4 - 2x

The 2x and -2x cancel each other out, so we are left with: x^2 - 4

Therefore, the product of (x-2)(2+x) is x^2 - 4.

е) (c+a)(a-c)

Let's multiply these two binomials:

First terms: c * a = ac

Outer terms: c * -c = -c^2

Inner terms: a * a = a^2

Last terms: a * -c = -ac

Combining the like terms: ac - c^2 + a^2 - ac

The ac and -ac cancel each other out, so we are left with: a^2 - c^2

Hence, the product of (c+a)(a-c) is a^2 - c^2.

To summarize: а) (y-3)(y+3) = y^2 - 9 б) (1-x)(1+x) = 0 в) (m-n)(m+n) = m^2 - n^2 г) (x+y)(x-y) = x^2 - y^2 д) (x-2)(2+x) = x^2 - 4 е) (c+a)(a-c) = a^2 - c^2