Question

1)(x+5)(x-5)2)(a-4)(4+a)3)(2b+a)(2b-a)4)(y+6x)(6x-y)

Answer 1

1. Х^2-25
2.а^2-16
3.4в^2-а^2
4. 36х^2-у^2

Answer 2

1) (x+5)(x-5): To expand this expression, we can use the FOIL method, which stands for First, Outer, Inner, Last.

First, we multiply the first terms of each binomial: x * x = x^2.

Outer, we multiply the outer terms of each binomial: x * -5 = -5x.

Inner, we multiply the inner terms of each binomial: 5 * x = 5x.

Last, we multiply the last terms of each binomial: 5 * -5 = -25.

Now, we combine these terms together to get the expanded form: (x+5)(x-5) = x^2 - 5x + 5x - 25.

Simplifying the expression, we can see that the middle terms cancel each other out: (x+5)(x-5) = x^2 - 25.

Therefore, the expanded form of (x+5)(x-5) is x^2 - 25.

2) (a-4)(4+a): Using the same FOIL method, we can expand this expression as well.

First, we multiply the first terms of each binomial: a * 4 = 4a.

Outer, we multiply the outer terms of each binomial: a * a = a^2.

Inner, we multiply the inner terms of each binomial: -4 * 4 = -16.

Last, we multiply the last terms of each binomial: -4 * a = -4a.

Combining these terms together, we get: (a-4)(4+a) = 4a + a^2 - 16 - 4a.

Simplifying the expression, we see that the "4a" and "-4a" terms cancel each other out: (a-4)(4+a) = a^2 - 16.

So, the expanded form of (a-4)(4+a) is a^2 - 16.

3) (2b+a)(2b-a): Using the FOIL method once again:

First, we multiply the first terms of each binomial: 2b * 2b = 4b^2.

Outer, we multiply the outer terms of each binomial: 2b * -a = -2ab.

Inner, we multiply the inner terms of each binomial: a * 2b = 2ab.

Last, we multiply the last terms of each binomial: a * -a = -a^2.

Combining these terms together, we get: (2b+a)(2b-a) = 4b^2 - 2ab + 2ab - a^2.

Simplifying the expression, we can see that the "2ab" and "-2ab" terms cancel each other out: (2b+a)(2b-a) = 4b^2 - a^2.

The expanded form of (2b+a)(2b-a) is 4b^2 - a^2.

4) (y+6x)(6x-y): Once again, using the FOIL method:

First, we multiply the first terms of each binomial: y * 6x = 6xy.

Outer, we multiply the outer terms of each binomial: y * -y = -y^2.

Inner, we multiply the inner terms of each binomial: 6x * 6x = 36x^2.

Last, we multiply the last terms of each binomial: 6x * -y = -6xy.

Combining these terms together, we get: (y+6x)(6x-y) = 6xy - y^2 + 36x^2 - 6xy.

Simplifying the expression, we can see that the "6xy" and "-6xy" terms cancel each other out: (y+6x)(6x-y) = 36x^2 - y^2.

Therefore, the expanded form of (y+6x)(6x-y) is 36x^2 - y^2.

I hope this helps! Let me know if you have any further questions.